Novel Methods for Fabrication of
Non-Close-Packed Structures through Colloidal
MASSACHUSETTS INSITTUTE
OF TECHNOLOGY
Self-Assembly
by
JUN 16 2010
Vyom Sharma
LIBRARIES
Submitted to the Department of Materials Science and Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
ARCHNES
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2010
© Massachusetts Institute of Technology 2010. All rights reserved.
A uthor ................. v......
. .. ...............................
Department of Materials Science and Engineering
September 3, 2009
C ertified by .............
.
.....................................
J
Yet-Ming Chiang
r of Ceramics
Thesis
pervisor
C ertified by .
...........................
W. Craig Carter
Professor of Materials Science and Engineering, MacVicar Faculty
I
Thesis SuFellow
.//(~Thesis
Supervisor
........
Christine Ortiz
Chair, Departmental Committee on Graduate Students
Accepted by ....
2
Novel Methods for Fabrication of Non-Close-Packed
Structures through Colloidal Self-Assembly
by
Vyom Sharma
Submitted to the Department of Materials Science and Engineering
on September 3, 2009, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
Colloidal dispersions are usually stabilized by interparticle electrostatic repulsion.
However, strong electrostatic potentials prevent nucleation of new structures. When
the electrostatic potential is strongly attractive, particles coagulate into a disordered
structure; if it is strongly repulsive, known processes can order them into a closepacked structure. Driven by the need to make tailored structures, researchers have
focused on circumventing electrostatics to nucleate and stabilize newer structures.
Yet most colloidal systems of interest are strongly charged. Reducing the electrostatic potential of a system may create only unstable structures without long-range
order. In this thesis, electrostatic interaction between strongly charged particles is
exploited to make novel structures. It is shown that -with an added steric component in the interaction potential- oppositely charged particles, which undergo rapid
coagulation otherwise, can be arranged into stable, long-range ordered structures.
Compared to their like-charged counterparts, these structures have greater stability
due to an attractive electrostatic potential. It is shown that an entire class of surfactants, amphiphilic non-ionic surfactants, can be used to stabilize an oppositely
charged particle system. Stabilizing these systems, allows for the nucleation of newer
structures. For instance, it is shown that a non-close-packed arrangement of positive
particles can be obtained on a layer of negatively charged particles. Creating such
non-close-packed 2D structures on a template is essential for creating 3D non-closepacked structures. Indeed, it is shown that at high Debye lengths, by varying the
concentration of particles in a suspension of like-charged colloids, electrostatic repulsion among particles can stabilize "sparse" structures. In these structures, particles
occupy only a few of the many sites that are available to them. Yet, they form an
ordered structure. Nuclei of a sparser structure are assembled at higher Debye length
and lower particle concentration. Monte Carlo simulations confirm that these structures are stabilized by electrostatic repulsion when particle concentration is low. It
is shown that the remaining sites in a sparse structure can be filled by a different
particle type. By replicating this process of 2D heterostructure formation, layer by
layer, and removing one kind of particle in the last step of the process, a two-layer
non-close-packed structure is obtained.
Thesis Supervisor: Yet-Ming Chiang
Title: Kyocera Professor of Ceramics
Thesis Supervisor: W. Craig Carter
Title: Professor of Materials Science and Engineering, MacVicar Faculty Fellow
Acknowledgments
Completion of a PhD thesis is a big milestone in a person's life. For me, this couldn't
have been possible without the help and support of many people. This space is
insufficient to thank all of them.
Foremost, I want to thank the one guiding light which has shown me the way all
my life and is truly the gift of God, "Shrimad Bhagwat Gita". I am fortunate enough
for extending my profound gratitude to this book of knowledge. This explained and
taught me the art of living for the enrichment of my mind and heart. This enabled me
to seek guidance from the superpowers at the time of confusion for the procurement
of processed knowledge and flawless decision.
Next, I want to thank my mother. I definitely would not have been here without
her single minded efforts and innumerable sacrifices. Completion of this thesis is truly
a testimony to the efforts that she has put bringing me up and I want to dedicate
this thesis to her.
I wish I could have met her before, but my wife is indeed the one person who has
been with me all along in this ride. I surely will never be able to thank her enough
for this. Her support and love were crucial in times of immense pressure. I hope to
do bigger and greater things for her.
My thesis advisors, Prof. Yet-Ming Chiang and Prof. Craig Carter have been the
most thoughtful and inspiring advisors that I could have imagined. They encouraged
me to believe in my ideas and supported me all these years. I am glad that with
their help, I was able to finish this work and thank them for their support. Prof.
Francesco Stellacci and Prof. Karl Berggren provided crucial insight into the data
analysis. This helped me analyze the data and map the trends in the experiments,
clearly. Prof. Berggren also granted me access to Nano Structures Laboratory(NSL),
and this work could not have been completed without this. I specially want to thank
Jim Daley, for being there whenever there were problems at NSL.
My sister and brother-in-law were there for me when I needed them the most and
I am thankful for their support. I want to thank them for their help through these
years.
My parents-in-law have been very supportive and helpful through this crucial time
and I want to thank them for their blessings and guidance.
My collaborators during this thesis, Prof. C.C. Wong, Dr. Deying Xia, Dr.
Qingfeng Yan, and Dr. Yaw Koon Woh, were very helpful. I want to thank all
Chiang and Carter group members for making my stay here very fulfilling. I had
many useful discussions with Dr. Garry Maskaly, Dr. Ming Tang, and Dr. Rick
Rajter. I also want to thank Rubner group for allowing me to use their facilities. I
want to thank my MADMEC and 1OOK team members.
Clearly, this space is limited. As a result, I apologize for not mentioning the names
of many others who were a key to finishing this thesis.
Contents
1 Motivation and Layout of the Thesis
1.1
Layout of the Thesis ......
...........................
2 Colloidal Forces and Methods of Self-Assembly
25
27
29
2.1
Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.2
Interactions between Colloidal Particles . . . . . . . . . . . . . . . . .
32
2.2.1
Van der Waals Interaction . . . . . . . . . . . . . . . . . . . .
32
2.2.2
Electrostatic Interaction . . . . . . . . . . . . . . . . . . . . .
34
2.2.3
Steric Interaction . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.2.4
Hydrophobic Interaction . . . . . . . . . . . . . . . . . . . . .
42
2.3
Stability of Colloidal Dispersions: DLVO Theory . . . . . . . . . . . .
43
2.4
Self-assembly of Colloids . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.4.1
Methods of Self-assembly . . . . . . . . . . . . . . . . . . . . .
46
2.4.2
Directed Self-assembly . . . . . . . . . . . . . . . . . . . . . .
48
3 Controlled Ordering of Oppositely Charged Colloidal Particles
51
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.2
Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.2.1
Colloidal suspensions . . . . . . . . . . . . . . . . . . . . . . .
53
3.2.2
Surfactants
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.2.3
Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.2.4
Template
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.2.5
Spin-coating . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Dip-coating . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
Spin-coating of Oppositely Charged Colloids . . . . . . . . . . . . . .
61
3.3.1
Surfactantless spin-coating of colloidal particles . . . . . . . .
61
3.3.2
Spin-coating of colloidal particles with non-ionic surfactant . .
62
3.4
Dip-Coating of Oppositely Charged Colloids . . . . . . . . . . . . . .
67
3.5
Theoretical Calculations . . . . . . . . . . . . . . . . . . . . . . . . .
71
3.6
Colloidal Self-assembly on Charged Substrates: Role of Hydrophobicity
75
3.7
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
3.2.6
3.3
4 Layer-by-Layer Self-Assembly of Non-Close-Packed Heterostructures 79
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
4.2
Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.3
4.4
4.2.1
M aterials
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.2.2
Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.2.3
Template Preparation
. . . . . . . . . . . . . . . . . . . . . .
83
4.2.4
Colloidal Assembly . . . . . . . . . . . . . . . . . . . . . . . .
84
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
. . . . . . . . . . . . . . . .
85
4.3.1
Li-PS: Sparse Polystyrene Layer
4.3.2
Results and Discussion: Mechanism of Sparse Structure Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.3.3
Discussion: Conditions for Sparse Structure Formation
. . . .
93
4.3.4
Li-Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.3.5
L2-P S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.6
L2-Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.7
L 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5 Stick and Slip During Convective Assembly
117
6 Monte Carlo Simulations of Sparse Ordering
121
6.1
Simulation Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7 Conclusions and Outlook
139
10
List of Figures
2-1
SEM image of the top view and cross-section of a colloidal crystal of
polystyrene particles. The particles assemble in a face centered cubic
(f.c.c.) structure with (111) orientation relative to the substrate. . . .
45
. . . . . . . . . . . . . .
48
2-2
Schematic of a convective assembly process.
3-1
A schematic for the Lloyd's Mirror Interference Lithography set-up
.
56
3-2
A schematic for the procedure to fabricate the template . . . . . . . .
57
3-3
SEM image of 100 nm diameter positively charged PS sphere suspension (0.25-w/v%) spin-coated at 3000 rpm on a substrate made from
420 nm diameter negatively charged PS spheres . . . . . . . . . . . .
3-4
60
100 nm diameter positively charged PS sphere suspension (1.0-w/v%)
spin-coated at 3000 rpm on a substrate made from 420 nm diameter
negatively charged PS spheres . . . . . . . . . . . . . . . . . . . . . .
3-5
60
100 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in isopropanol (80%) - DI water (20%) spin-coated at 3000 rpm on a
substrate made from 420 nm diameter negatively charged PS spheres
3-6
63
100 nm diameter positively charged PS sphere suspension (0.25-w/v%)
in DI water with Triton X-100, spin-coated at 3000 rpm on a substrate
made from 420 nm diameter negatively charged PS spheres for 60 seconds 64
3-7 Pair distribution function (pdf) for small particles from fig. 3-6, o is
the diameter of the small sphere . . . . . . . . . . . . . . . . . . . . .
64
3-8
210 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in DI water, spin-coated at 3000 rpm on a substrate made from 420
nm diameter negatively charged PS spheres for 60 seconds . . . . . .
3-9
65
Pair distribution function (pdf) for small particles from fig. 3-8, U is
the diameter of the small sphere . . . . . . . . . . . . . . . . . . . . .
65
3-10 100 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in DI water, spin-coated at 6000 rpm on a substrate made from 420
nm diameter negatively charged PS spheres for 60 seconds . . . . . .
66
3-11 Pair distribution function (pdf) for small particles from fig. 3-10, o- is
the diameter of the small sphere . . . . . . . . . . . . . . . . . . . . .
66
3-12 SEM image of a larger domain with LS 6 ordering . . . . . . . . . . .
67
3-13 SEM image of a larger domain with LS 2 ordering . . . . . . . . . . .
68
3-14 140 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in DI water, spin-coated at 3000 rpm on a substrate made from 250
nm diameter negatively charged PS spheres for 60 seconds. The layer
of 250 nm particles were assembled on a template with holes arranged
in (100) symmetry, through convective assembly. . . . . . . . . . . . .
68
3-15 A schematic showing the first two layers for a layer-by-layer assembly
of ZnS-type structure. Green spheres represent positive PS particles in
the second layer and red spheres represent negative PS particles from
the first layer. In the second layer only half of the total interstices are
occupied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3-16 A schematic showing the first three layers for the layer-by-layer assembly of ZnS-type structure. Green spheres represent positive PS
particles in the second layer and red spheres represent negative PS
particles. The position of negative particles in the third layer is shown
in translucent blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
3-17 A schematic showing the first four layers for a layer-by-layer assembly
of ZnS-type structure. Green spheres represent positive PS particles
in the fourth layer and red spheres represent negative PS particles . .
70
3-18 SEM image after a suspension of 0.1-w/v% 140 nm diameter positively charged amidine functionalized PS spheres with Triton X-100,
deposited on a substrate of 420 nm negatively charged PS particles
which were arranged in f.c.c. pattern with (111) orientation.
The
dip-coating lasted for 60 seconds . . . . . . . . . . . . . . . . . . . . .
71
3-19 Normalized electrostatic force (relative to the Brownian force) and electrostatic energy (relative to kBT ) with respect to the position of a 100
nm positive PS sphere moving on the surface of one of the 420 nm
negative PS spheres, which are packed into close packed with fcc (111)
orientation.
Salt concentration has been assumed to be 0.001 mM
whereas the surface charge density for each kind of sphere has been
assumed to be identical to the value supplied by the manufacturer.
The calculation was done by solving the linearized Poisson Boltzmann
equation for a system of 7 negative PS spheres and one positive PS
sphere through the PoissonBoltzmann solver. For position 1, the positive PS sphere sits in the crevice formed by 3 negative PS spheres.
02 =
45',03 = 55, ,4=
65',60
.
. . . . . . . . . .73
= 750 and 66 = 90 .
3-20 DLVO (van der Waals + electrostatic) interaction energy (in red) and
DLVO + steric interaction energy (in blue). The above calculations
are for a negative 420 nm PS and a positive 100 nm PS approaching
each other in water. For the steric interaction,
and X = 0.45
#=
0.10, vi = 0.03nm 3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3-21 DLVO + steric interaction as a function of the adsorbed surfactant
volum e fraction
4-1
#
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
SEM image of a silicon template, which has holes arranged in a pattern
with (100) symmetry. The holes were 45 nm deep. This template was
created according to the procedure described in section 3.2.4 . . . . .
83
4-2 Contact angle measurement on a bare silicon template after exposure
to oxygen plasma. The contact angle was 0.80 .
. . . . . . . . . . . .
84
4-3 Schematic showing the different kinds of ordering seen on the template. 85
4-4 SEM image of a template after convective assembly of PS particles
from a 0.025-v/v% aqueous suspension. Due to stick and slip of the
meniscus, the particles assemble in bands, separated by regions on
the template without any particles. In this image, bright regions are
bands of PS particles, whereas dark regions are regions on the template
without any particles . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4-5 SEM image of a template, after convective assembly of 250 nm PS
particles from a 0.01-v/v% aqueous suspension. The withdrawal speed
of the suspension was 46.1 pm/min at 35'C. K-1 was 204 nm. This
was inferred from conductivity measurement of the solvent. As seen
in this image, particles arrange in a sparse pattern. The inset shows a
schematic arrangement of particles on the template: red circles denote
particles and open circles denote empty holes. Due to the low concentration of the particles in suspension, narrow bands of PS particles
assemble on the template. . . . . . . . . . . . . . . . . . . . . . . . .
87
4-6 SEM image of a template, after convective assembly of 250 nm PS
particles from a 0.025-v/v% aqueous suspension. The withdrawal speed
of the suspension was 46.1 pm/min at 35'C. K-1 was 204 nm. This
was inferred from conductivity measurement of the solvent. As seen
in this image, particles arrange in a sparse pattern. The inset shows a
schematic arrangement of particles on the template: red circles denote
particles on holes and open circles denote empty holes. . . . . . . . .
88
4-7 SEM image of a template after convective assembly of 250 nm PS
particles from a 0.1-v/v% aqueous suspension. The withdrawal speed
of the suspension was 46.1 pm/min at 35'C. r-
1 was
204 nm. This was
inferred from conductivity measurement of the solvent. Due to high
concentration of PS particles in the suspension, they fill all the holes
in the template. The inset shows a schematic arrangement of particles
on the template. Red circles denote PS particles on holes.
. . . . . .
89
4-8 Plot of the pair distribution function for the arrangement of 250 nm
PS particles in fig. 4-5 and fig. 4-6. o- is the diameter of the sphere
.
89
4-9 Plot of the pair distribution function for the arrangement of 250 nm
PS particles in fig. 4-7. o- is the diameter of the sphere . . . . . . . .
90
4-10 SEM image of the cross-section of a template with 250 nm PS particles
ordered in Li-PS arrangement . . . . . . . . . . . . . . . . . . . . . .
90
4-11 SEM image after convective assembly of 250 nm PS particles from a
0.025-v/v% aqueous suspension. The withdrawal speed of the suspension was 46.1 pm/min at 35'C. ,-1 was 30 nm. This was inferred
from conductivity measurement of the solvent. Random filling may be
associated with the reduced Debye length. . . . . . . . . . . . . . . .
91
4-12 Plot of the pair distribution function for the arrangement of 250 nm
PS particles in fig. 4-11. o- is the diameter of the sphere. Due to
low r-', the arrangement shows short-range order compared to the
arrangement of particles in fig. 4-6 . . . . . . . . . . . . . . . . . . .
91
4-13 SEM image of a large area of the template after convective assembly of
250 nm PS particles from their 0.025-v/v% aqueous suspension. The
withdrawal speed of the suspension was 46.1 pm/min at 35'C. rn- 1 was
204 nm. This was inferred from conductivity measurement of solvent.
This image shows a Li-PS band where PS particles are arranged akin
to their arrangement in fig. 4-6. Thus, typical Li-PS domains were
15 pm wide along the direction of withdrawal of the suspension and
hundreds of pm large, perpendicular to it. . . . . . . . . . . . . . . .
4-14 Variation of Aband and
6
band
92
when PS particles were assembled onto tem-
plates, fixed at different orientations relative to the direction of withdrawal of the suspension. The suspension was withdrawn at 46. lpm/min
at 350 C. .......
4-15 Variation of
#p,,arse
..................................
93
when PS particles were assembled onto templates,
fixed at different orientations relative to the direction of withdrawal of
the suspension. The suspension was withdrawn at 46.lpm/min at 35 0 C. 94
4-16 Contact angle measurement on Li-PS substrate, after it was exposed
to oxygen plasma for 10 seconds. The contact angle of water was 4.7'
96
4-17 SEM image of a template with 250 nm PS particles arranged on the
template. This image was taken after silica particles were assembled
from a 0.025-v/v% ethanol suspension, on a substrate with 250 nm PS
particles arranged on the template. PS particles are partially soluble
in ethanol. As a result, they swell to 350 nm and coalesce . . . . . . .
97
4-18 SEM image showing the arrangement of 250 nm silica and PS particles, after silica particles were assembled from a 0.025-v/v% aqueous
suspension, at 50'C, on Li-PS substrate. The speed of withdrawal of
the suspension was 46.1 pm/min. This kind of order is referred to as
LI. PS particles appear dark and silica particles appear bright. The
contrast is due to different material composition . . . . . . . . . . . .
98
4-19 SEM image of a large area with Li ordering. This region is made of
dark 250 nm PS particles arranged in every other hole and bright 250
nm silica particles filling the remaining holes. The contrast is due to
different material composition. Typical bands with Li order were 8
pim wide along the direction of withdrawal of the suspension, and tens
of micrometers large, perpendicular to it . . . . . . . . . . . . . . . .
99
4-20 SEM image of a template after convective assembly of 250 nm PS
particles from their 0.01-v/v% aqueous suspension. The withdrawal
speed of the suspension was 46.1 pm/min at 35'C and ,-1 was 250
nm. This was inferred from conductivity measurement of the solvent.
Due to low concentration of PS particles in the suspension and due
to high K-1 , sparser pattern was stabilized by electrostatic repulsion
between particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4-21 SEM image of 250 nm bright silica particles and 250 nm dark PS
particles arranged on a template. Silica particles were deposited on
a template with PS particles arranged in a sparser pattern, shown in
fig. 4-20. Silica particles were deposited from a 0.025-v/v% aqueous
suspension at 50'C. The suspension was withdrawn at 46.1 pm/min . 101
4-22 SEM image of a large area with 250 nm PS particles arranged in a
sparse pattern in the second layer.
Li order.
The underlying first layer had
PS particles were deposited from a 0.025-v/v% aqueous
suspension at 23.3 pm/min and 35'C, through convective assembly.
Typical bands with L2-PS order were 5 pm wide.
. . . . . . . . . . . 102
4-23 SEM image of a region with 250 nm PS particles arranged in a sparse
pattern on the second layer. The underlying, first layer had Li order.
PS particles were deposited from a 0.025-v/v% aqueous suspension at
23.3 [tm/min and 350 C, through convective assembly . . . . . . . . . 103
4-24 PS particles in L2-PS in fig. 4-23, are colored in green. Dull green discs
denote vacancies, whereas bright green discs denote PS particles. Here,
L2-PS domain is made of three L2-PS grains. These are represented by
coloring the rim of the discs differently. Discs with identically colored
rims belong to the same grain . . . . . . . . . . . . . . . . . . . . . . 103
4-25 SEM image of a region with 250 nm PS particles arranged in a sparse
pattern in the second layer. In the first layer PS particles occupy all
the holes. Larger domains of PS particles with sparse ordering were
observed when the underlying layer was made solely of PS particles.
Here, PS particles were deposited in the second layer from a 0.025-v/v%
aqueous suspension at 23.3 pm/min and 35'C, through convective assem bly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4-26 Variation of Asilica.band and
6
silica-band for silica particles after dip-
coating in different suspensions of PAH . . . . . . . . . . . . . . . . . 106
4-27 Variation of
dL2
after dip-coating in different suspensions of PAH . . 107
4-28 SEM image after 250 nm silica particles were deposited in the second
layer, from a 0.025-v/v% aqueous suspension at 50'C and 46.1 pm/min,
through convective assembly. Prior to silica deposition, the substrate
was dipped in 1 mg/ml suspension of PAH for 10 minutes . . . . . . . 107
4-29 Identical SEM image to fig. 4-28. PS particles in the second layer are
colored green and silica particles in the second layer are colored red,
for better visual contrast. The colored particles form a L2 domain . . 108
4-30 SEM image after 250 nm silica particles were deposited in the second
layer, from a 0.025-v/v% aqueous suspension at 50'C and 46.1 pm/min,
through convective assembly. Prior to silica deposition, the substrate
was dipped in 3 mg/ml suspension of PAH for 5 minutes . . . . . . . 108
4-31 Identical SEM image to fig. 4-30. PS particles in the second layer are
colored green and silica particles in the second layer are colored red,
for better visual contrast. The colored particles form a L2 domain . . 109
4-32 SEM image after 250 nm silica particles were deposited in the second
layer, from a 0.025-v/v% aqueous suspension at 50'C and 46.1 pm/min,
through convective assembly. Prior to silica deposition, the substrate
was dipped in 7 mg/ml suspension of PAH for 5 minutes. Note that a
negatively charged silica particle is perched on top of another particle
in the first layer. This may indicate that charge reversal took place for
particles in the first layer, after dipping in the 7 mg/ml suspension of
PA H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-33 Variation of Asilica-band and
6
silica-band
110
after deposition of silica particles
at different relative humidities . . . . . . . . . . . . . . . . . . . . . . 111
4-34 Variation of <L2 after deposition of silica particles at different relative
hum idities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4-35 SEM image showing a band of 250 nm silica particles arranged in a
3D non-close-packed structure. PS particles were removed from the
sample by exposure to oxygen plasma.
. . . . . . . . . . . . . . . . . 113
4-36 SEM image of 250 nm silica particles arranged in a 3D non-closepacked structure. PS particles were removed from the original sample
by exposure to oxygen plasma . . . . . . . . . . . . . . . . . . . . . . 114
4-37 SEM image of a cross-section of a template with 250 nm silica particles
arranged in a 3D non-close-packed structure . . . . . . . . . . . . . . 114
5-1 Plot of the surface tension forces during convective assembly. The
suspension is withdrawn at a rate vz.
6-1
Plot of
T
. . . . . . . . . . . . . . . . . . 118
across ln(c) - T landscape, for the arrangement of 140 nm
particles, when r-1=30 nm . . . . . . . . . . . . . . . . . . . . . . . . 125
6-2
Plot of r across ln(c) - T landscape, for the arrangement of 140 nm
particles, when r-1=100 nm . . . . . . . . . . . . . . . . . . . . . . . 126
6-3
Plot of
T
across ln(c) - T landscape, for the arrangement of 140 nm
particles, when r-1=204 nm . . . . . . . . . . . . . . . . . . . . . . . 126
6-4 Plot of r across ln(c) - T landscape, for the arrangement of 250 nm
particles, when ,-1=30 nm . . . . . . . . . . . . . . . . . . . . . . . . 127
6-5
Plot of r across ln(c) - T landscape, for the arrangement of 250 nm
particles, when ,-1=100 nm . . . . . . . . . . . . . . . . . . . . . . . 127
6-6
Plot of -r across in(c) - T landscape, for the arrangement of 250 nm
particles, when ,-1=204 nm . . . . . . . . . . . . . . . . . . . . . . . 128
6-7
Plot of r across in(c) - T landscape, for the arrangement of 500 nm
particles, when ,-1=30 nm . . . . . . . . . . . . . . . . . . . . . . . . 128
6-8
Plot of r across ln(c) - T landscape, for the arrangement of 500 nm
particles, when r-1=100 nm . . . . . . . . . . . . . . . . . . . . . . . 129
6-9
Plot of
T
across in(c) - T landscape, for the arrangement of 500 nm
particles, when ,-1=204 nm . . . . . . . . . . . . . . . . . . . . . . . 129
6-10 (a)Arrangement of 140 nm particles at K-=204 nm, ln(c)=40.1 and
T=1100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at n-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that unlike at ,- 1 =204
nm, at ,- 1=30 nm, all sites on the template are occupied.
. . . . . . 131
6-11 (a)Arrangement of 140 nm particles at K-1 =204 nm, lin(c)=40.1 and
T=3100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at --1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that unlike at
nm, at K1=30 nm, all sites on the template are occupied.
K-1=204
. . . . . . 131
6-12 (a)Arrangement of 140 nm particles at K-1=204 nm, ln(c)=40.1 and
T=5100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at 81=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that at
K.1=30
nm all
sites on the template are occupied; many domains where all sites are
occupied, are also stabilized for
-1=204 nm.
. . . . . . . . . . . . . 132
6-13 (a)Arrangement of 140 nm particles at K-1=204 nm, ln(c)=40.1 and
T=7100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at K-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that at all
K-1
values,
all sites on the template are occupied. . . . . . . . . . . . . . . . . . . 132
6-14 (a)Arrangement of 250 nm particles at r- 1=204 nm, ln(c)=40.1 and
T=1100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at r-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that unlike at ,-1=204
nm, at ,-1=30 nm, all sites on the template are occupied.
. . . . . . 133
6-15 (a)Arrangement of 250 nm particles at r-1=204 nm, ln(c)=40.1 and
T=3100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at K-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that unlike at ,- 1=204
nm, at r--1=30 nm, all sites on the template are occupied.
. . . . . . 133
6-16 (a)Arrangement of 250 nm particles at K-1=204 nm, ln(c)=40.1 and
T=5100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at K-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that at ,-1=30 nm all
sites on the template are occupied; many domains where all sites are
occupied, are also stabilized for ,- 1 =204 nm.
. . . . . . . . . . . . . 134
6-17 (a)Arrangement of 250 nm particles at r-1=204 nm, ln(c)=40.1 and
T=7100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at K-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that at all ,-' values,
all sites on the template are occupied. . . . . . . . . . . . . . . . . . . 134
6-18 (a)Arrangement of 500 nm particles at K-1=204 nm, ln(c)=40.1 and
T=1100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at K-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that unlike at K-1=204
nm, at ,-1=30 nm, all sites on the template are occupied.
. . . . . . 135
6-19 (a)Arrangement of 500 nm particles at ,-1=204 nm, ln(c)=40.1 and
T=3100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at K-1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that unlike at ,-1=204
nm, at K-1=30 nm, all sites on the template are occupied. . . . . . . 135
6-20 (a)Arrangement of 500 nm particles at K-1=204 nm, ln(c)=40.1 and
T=5100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at
--1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that at
-1=30 nm all
sites on the template are occupied; many domains where all sites are
occupied, are also stabilized for ,-1=204 nm.
. . . . . . . . . . . . . 136
6-21 (a)Arrangement of 500 nm particles at K-1=204 nm, ln(c)=40.1 and
T=7100K. (b)Pair Distribution Function (PDF) for the particles on
the template, in (a), is plotted in red. For comparison, PDF for the
arrangement of particles at
--1=100 nm and 30 nm are plotted in blue
and green respectively. These PDF plots show that at all -1 values,
all sites on the template are occupied. . . . . . . . . . . . . . . . . . . 136
List of Tables
3.1
Variation of Debye length with increasing NaCl concentration in water
3.2
Variation of Triton-X 100 coverage on Polystyrene with bulk concentration of Triton- X 100, as determined by QCM . . . . . . . . . . . .
4.1
Variation in Aband,
#sparse,
and
6
band
72
at different Debye lengths and
concentrations for 250 nm PS particles . . . . . . . . . . . . . . . . .
4.2
59
87
Formation of the sparse structure at different speeds of withdrawal of
the suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 105
4.3
Summary of Dip-coating in PAH
4.4
Characteristics of Li-PS bands from carboxyl and sulphate functionalized PS particles
95
. . . . . . . . . . . . . . . . . . . . . . . . . . . .111
24
Chapter 1
Motivation and Layout of the
Thesis
Colloidal dispersions were regarded as ideal systems to experimentally simulate molecular behavior [1, 2, 3]. Thus, the behavior of colloidal particles in suspension has been
the subject of several studies [4, 5]. It is only in the last few years that researchers
have come to realize the significance of colloidal crystals. These ordered aggregates of
colloidal particles have shown a remarkable promise as sensors [6, 7, 81 and molecular
filters [9, 10], and most notably as photonic crystals [11, 12, 13].
Colloidal self-assembly on bare substrates produces close-packed structures. As a
result, templates are required to nucleate and stabilize non-close-packed structures.
Recently, Santamaria et al. demonstrated that a diamond cubic complete photonic
band gap (CPBG) structure is produced when polymer and silica particles are robotically placed, one by one, on a template [14]. Since this process is lengthy and expensive, methods that rely on self-assembly are favored. In the last few years, researchers
have used mildly repulsive and hard-sphere potentials to make perfect close-packed
crystals [15]-[19]. Others have proposed that templated assembly of ionic colloidal
crystals (ICCs), in a dispersion with mildly attractive electrostatic potential, may be
able to create CPBG photonic crystals [20, 21].
In this thesis, novel self-assembly methods are used to order strongly charged particles. These methods utilize electrostatic interaction to nucleate newer structures. It
is shown that the motif of these structures can serve as a starting point for generating
the complex periodic architectures, which are needed for integrated photonic crystal
applications.
The objective of this thesis is twofold. The first objective is to outline methods
that can be used to create stable aggregates from strongly charged particles, whether
they are similarly or oppositely charged. The second objective is to utilize these methods to create binary and non-close-packed structures through directed self-assembly.
It is shown that when particles are oppositely charged, a steric force is necessary
to order them into stable structures [22].
Binary colloidal crystals are nucleated
and show greater stability compared to their like-charged counterparts. Therefore,
they are better candidates for making low-volume and non-close-packed architectures.
Findings from this study are contrary to published reports, which state that only
mild electrostatic attraction can nucleate stable and ordered structures [23].
It is
also shown that like-charged particles order in a non-close-packed arrangement on
a close-packed substrate of oppositely charged particles. Clearly, greater attraction
between particles leads to a more stable structure. Stability of these structures is
verified through theoretical calculations.
When particles are similarly charged, it is shown that a suitable 2D template can
be used to nucleate non-close-packed structures [24]. These structures are sparsely
ordered*. In other words, the particles occupy only a few of the sites available to them.
Yet, they form an ordered structure. Experiments and computational Monte Carlo
simulations show that a high Debye length in the solvent and a low concentration of
particles in the suspension are necessary requirements for nucleating sparse structures.
If the Debye length is small, thermal motion would prevent the nucleation of sparse
domains. It is shown that sparse arrangement of particles can be exploited to make
a non-close-packed two-layered structure.
*In this thesis, sparse ordering refers to an arrangement of particles, such that they are ordered
with a (110) orientation (with respect to the underlying substrate) on a template with holes arranged
in (100) orientation. Additionally, only 50% of the holes on the template are occupied.
1.1
Layout of the Thesis
Chapter 2 provides a background of colloidal forces. Later in the chapter, a brief literature survey of colloidal self-assembly is presented. Thereafter, a few self-assembly
and directed self-assembly methods, relevant to this thesis, are discussed.
Chapter 3 discusses a simple and rapid layer-by-layer method to order strongly
and oppositely charged particles. By using a spin-coating method, stable LS 2 and LS 6
structures are nucleated. Later in the chapter, a dip-coating method is used to make
two layers of a non-close-packed structure. Theoretical calculations show that, using
oppositely charged particles creates more stable structures compared to similarly
charged particles. At the end of this chapter, the role of hydrophobic interaction
during self-assembly of charged particles on charged substrates, is discussed.
Chapter 4 discusses the formation of a sparse layer of particles on a template,
with holes arranged in (100) symmetry. It is shown that the sparse order depends
on the Debye length of the solvent and concentration of particles in the suspension.
Subsequently, a 2D heterostructure is formed by filling the unoccupied sites in the
sparse layer. Thereafter, the conditions and experiments for the formation of a twolayer heterostructure are discussed. It is shown that the removal of one type of particle
from this structure, leads to a two-layer structure with non-close-packed arrangement
of particles.
Chapter 5 reviews the mechanism behind stick and slip. Recently, a few methods
have been used to make colloidal crystals; in these methods there was no stick and slip
of the meniscus. In this chapter, the feasibility of these methods, such as LangmuirBlodgett (LB), to assemble a sparse pattern of particles, is discussed.
Chapter 6 discusses the results from Monte Carlo simulations. Conditions for the
arrangement of colloidal particles into sparse domains are discussed. The results from
these simulations show that the formation of sparse domains requires a large Debye
length in the solvent and a low concentration of particles in the suspension. Further,
conditions for the formation of sparsert domains are discussed.
tIn this thesis, sparser ordering refers to an arrangement of particles, such that they are ordered
with a (111) orientation (with respect to the underlying substrate) on a template with holes arranged
In Chapter 7, general conclusions and the scope of this thesis are discussed. In
the end, future directions for this work are outlined.
in (100) orientation. Additionally, only 25% of the holes on the template are occupied.
Chapter 2
Colloidal Forces and Methods of
Self-Assembly
Colloidal science has its roots in nineteenth-century discoveries concerning the behavior of minute particles suspended in a solvent. These systems are called colloidal
dispersions. A distinguishing feature of these dispersions is that the area of contact between the dispersed particles, and the solvent is relatively large. The name
"colloid" itself, comes from a study of colloidal dispersions by Thomas Graham in
1860. While looking at the passage of various solute dispersions through a dialysis
membrane, one kind of solute could not pass through. This solute (natural gum) led
Graham to coin the term "colloid" (after kolla, meaning natural gum). Presently,
colloidal dispersions are used all around us. Some notable examples are milk, paints,
etc.
Colloidal dispersions occur in many forms. The most widely used and studied are
dispersions of solids in liquids. The majority of conclusions from these studies are
applicable to dispersions of liquids in liquids (emulsions) and gases in liquids (foams).
However, those conclusions cannot be extended to dispersions of solids or liquids in
gases (aerosols). This thesis will be focused on dispersions of solids in liquids.
Particle size and shape are of considerable importance in setting the properties of
a colloidal system. A colloidal particle is a macroscopic entity, composed of a number
of atoms or molecules. The size of a colloidal particle ranges from a few nanometers
to hundreds of micrometers. However, the solute particles should be distinguishable
from the solvent molecules. As a result, the colloidal particles should be no smaller
than a nanometer.
Since the latter part of the
20
th
century, production of near-monodisperse disper-
sions has enabled many fundamental studies on colloidal particles. These particles
are uniform in size, shape, composition and surface properties. Spherical colloids in
particular, have been the most successful, best-established examples of monodisperse
systems. Elaborate schemes exist to synthesize spherical colloids from different materials. Driven by the minimization of interfacial energy, the spherical shape may
represent the simplest form into which a colloidal particle can develop for isotropic
surface energies. Experimental studies on spherical colloids have greatly enriched
our understanding of their light-scattering properties, interactions between colloidal
particles and their hydrodynamic properties.
In addition, spherical colloids represent ideal building blocks that can be readily
assembled into ordered structures. These ordered lattices are referred to as colloidal
crystals. Colloidal crystals allow for the observation of interesting functionality from
long-range ordered structures and not just the constituent particles. For example, the
beautiful colors of opal are the result of light diffraction from close-packed crystals
of silica colloids, which are themselves colorless. More recently, calculations have
shown that some colloidal crystal structures have a complete photonic band gap.
This has generated a lot of excitement and heralded newer ways of controlling crystal
growth orientation. As a result, newer ways of assembling colloidal crystals have
been proposed and almost all of these rely on controlling colloidal interaction. More
detailed discussions on these topics can be found elsewhere [25]-[32].
2.1
Brownian Motion
For very dilute suspensions, any interparticle interactions can be ignored. When
these dispersions are viewed under a microscope, the particles are seen to move in
a random motion. This is called Brownian motion. Brownian motion of particles
originates due to an uneven bombardment of the particles by solvent molecules. At
each step, the particles move in the direction of lower molecular densities. Due to
the random motion of water molecules, the directional motion of colloidal particles
fluctuates in a random manner and their velocities are governed by hydrodynamic
drag. For a spherical particle, the Stokes drag factor, so, is a function of the radius
of the sphere, a, and the viscosity of the fluid, 7, as shown in eq. 2.1:
(2.1)
s, = 67rqa.
The root mean squared (rms) velocity depends on the rms distance moved, Xrms, in
a time interval t, as:
(2.2)
Vrms = Xrmst.
The work done to move the particle is the hydrodynamic force,
fV
= VrmsSv, times
the distance xrms. This is the same as the thermal energy for the particle, kBT,
where kB is the Boltzmann's constant and T is the absolute temperature.
Two
important parameters can be derived from the above equations. The first is the
diffusion coefficient, D, shown in eq. 2.3:
x2
D =_-
t
=
kBT
.
(67rqa)
(2.3)
The above equation, eq. 2.3, is the Stokes-Einstein equation. The second parameter
is tc: the characteristic time it takes for a particle to diffuse a distance equal to its
radius, and is given by eq. 2.4:
tc = 67rqas3
kBT
(2.4)
The above equation is the Einstein-Smoluchowski equation. For an isolated 1 Am
particle at 20 C in water, the characteristic time is 0.5 seconds. For concentrated
colloidal dispersions, the movement of particles is influenced by neighboring particles
and interparticle forces (electrostatic, hydrodynamic or van der Waals).
2.2
2.2.1
Interactions between Colloidal Particles
Van der Waals Interaction
The van der Waals (vdW) interaction is the term used to describe the forces resulting
from interactions between dipoles, quadrapoles and multipoles. There are several
interactions that can occur, which are electrodynamic in origin; traditionally, these
are separated into three distinct forms. These are dipole-dipole interaction (Keesom
interaction) [33, 34, 35], dipole-induced dipole interaction (Debye interaction) [36, 37]
and induced dipole-induced dipole interaction (London interaction) [38, 39]. More
details about these forces can be obtained from an excellent review by French [40].
In general, colloidal particles do not have permanent dipoles. In that case, London
forces dominate the total van der Waals interaction and are briefly discussed below.
London forces describe the interaction that results between non-polar substances.
For colloids, the London interaction between two particles is assumed to the the sum
of the pairwise interactions of their atoms. The interaction energy can be written as
follows [39]:
(2.5)
U = -CL
The London constant, CL, is proportional to the ionization energy of the outer electrons, hvi, and the polarizability a:
CL oc hv 1 a 2 .
(2.6)
For two dissimilar molecules, this becomes:
CL
oc haia2
V11V12
.
(2.7)
In 1937, Hamaker published an article where he investigated the properties of van
der Waals interaction between large bodies [41].
The analysis in this paper was
far-reaching and showed that the strength of vdW interaction between large bodies is distinct from vdW interaction between molecules, which had been considered
previously. Hamaker used pairwise summation approximation to calculate these interactions. The idea in this approximation was that infinitesimal parts of large bodies
interact with one another according to the London equation. The total strength of
the vdW interaction between two bodies integrates over all such infinitesimal interaction terms. De Boer had shown previously [42] that the vdW interaction between
large planar slabs varies as the inverse of the square of separation distance between
them. As a result, vdW interaction came to be viewed as a longer-range interaction
than previously thought.
Of special importance in colloidal science is the interaction between two spherical
particles, 1 and 3, in a medium, 2. This is given by eq. 2.8 [43]:
Udw
A 123
2aia 3
a3 )2
6 r -(a+
r2
2aa
3
- (a - a3
)2
2
2
r
1nr
(a1 + a3 )2
- (ai - 3a )2
(28)
where r is the separation between particles with radii ai and a3 . The influence of the
intervening medium, 2, and material properties of the bodies, 1 and 3, is captured by
the Hamaker constant A 123 . From eq. 2.8, the interaction is divergent at contact. In
order to avoid this, a cut-off radius equal to the diameter of the solvent molecule is
used as the limiting distance for vdW interaction [44].
The Hamaker constant, A 123 , is of central importance in the analysis of vdW forces
between colloids. Although it is difficult to calculate in most instances, approximate
values of the Hamaker constant for materials in vacuum are 100-300 zJ for metals,
10-30 zJ for ionic materials and 3 zJ for hydrocarbons. In a solvent, these values are
greatly reduced due to screening of the interaction.
A 123 can be approximated from the Hamaker constant of materials in vacuum, as
shown in eq. 2.9 [28]:
A 123 = (VA11 -
A 22 )( A 33 -
A 2 2 ).
(2.9)
Early theories relied on pairwise additivity to calculate A 123 . This ignores the influence that neighboring atoms or molecules have on the interaction between any two
atoms. This interaction was treated exactly by Lifschitz [45]. According to his theory,
the Hamaker constant for the interaction of two media 1 and 3, across the medium
2, is given by eq. 2.10 [28]:
A123
3
-kBT(
~~w
4
where ei,
62
Ei - 62
C1 +
and
63
62
)(
es - 62
63 + 62
)+
o cE1(iv)
(7
3h
47
u
62 (iv)
e(iv) + 62 (iv)
-
)(
63 (iv) - E2 (iv)
Ei(iv) + e2 (iv)
) du, (2. 10)
are the static dielectric constants of the three media and e(iv) are
the values of c at imaginary frequencies. The first term gives the zero frequency energy
of van der Waals interaction and includes the Keesom and the Debye interaction.
The second term includes the contribution from London dispersion interaction. Two
important points should be noted about eq. 2.10: (i) first, the vdW force between any
two bodies in vacuum is attractive; (ii) second, vdW force between identical bodies
across all media is attractive, but may be attractive or repulsive for dissimilar bodies
in a medium.
2.2.2
Electrostatic Interaction
If vdW forces were to act alone, one might expect all suspended particles to coagulate. Normally, this does not happen because the suspended particles are stabilized
by electrostatic repulsion or steric repulsion, and do not coalesce. Electrostatic interaction is one of the most important stabilizing forces for charged colloidal dispersions.
Steric interaction is another, and is discussed later.
Interfaces between colloidal particles and ionic solutions, like water, almost always
acquire charge. This alters the concentration and spatial variation of free ions in solution. Several mechanisms have been identified for the charging of colloidal particles
[30]. Two relevant mechanisms for the purpose of this thesis are:
(i) The ionization of surface groups: for instance, ionization of surface hydroxyl
groups, shown in eq. 2.11, leads to negatively charged silica particles, whereas ionization of carboxyl groups (or sulfonic acid groups), shown in eq. 2.12, leads to
negatively charged latex particles. Ionization of amine and amidine groups leads to
positively charged latex particles.
Si - OH <-+ Si - O- + H+
(2.11)
-COOH
(2.12)
<-+
-COO-
+ H+
(ii) Adsorption or covalent bonding of charged entities from the suspension, onto
an uncharged surface. For instance, adsorption of amphiphilic polyelectrolytes charges
hydrophobic particles in water.
Poisson-Boltzmann Equation
Helmholtz gave the earliest treatment to describe the electrostatics related to a
charged particle in solution. He proposed a simple model, wherein a uniformly charged
sphere is surrounded by ions of opposite polarity, the counter-ions, in a uniform layer.
The counter-ions were assumed to be point charges. Later, a more complete treatment
of this was offered, wherein the finite size of the counter-ions and the diffuse nature of
the counter-ion distribution were taken into consideration [46]. The counter-ions (that
include particle counter-ions, ions from dissociated salts and ions from self-dissociated
solvent molecules) form an oppositely charged atmosphere in rapid thermal motion
close to the surface. This is called the diffuse double layer.
A model for the distribution of counter-ions, pg, depends on the electrostatic
potential, @b, and is given by eq. 2.13 [28]:
pg=pieo
p(
),
(2.13)
where
pi = Einizie.
(2.14)
Together with the Poisson equation, eq. 2.15:
-eco
2 $ = p,
(2.15)
this leads to the Poisson-Boltzmann equation (PBE), eq. 2.16:
S-2
-Ei
Er CO
exp(
kBT
),BTl
(2.16)
where ni is the number density of ions i of valence zi and e is the electronic charge.
PBE is one of the most important equations in colloidal science, and is the basis for
understanding the electrostatic interaction between colloidal particles.
Solutions of the Poisson-Boltzmann Equation
PBE is a second-order non-linear differential equation. It can be simplified by making
the following assumptions:
(i) Although there may be multiple salt species present in the solution, the ionic
concentration is dependent upon the majority salt component.
(ii) While a colloidal solution does not have an equal number of positive and
negative ions, the number of counter-ions from colloidal particles is small and can be
safely ignored. Moreover, the majority of salts are symmetric: that is, they have the
same magnitude for positive and negative ions.
With the above assumptions, the summation in eq. 2.16 reduces to a sum of two
exponentials. The resulting equation is shown in eq. 2.17:
znte
2 V)=
2 --
Er EO
ze@
sinh(
T)
2.7
(2.17)
kBT
The hyperbolic sine term in eq. 2.17 can be expanded as shown in eq. 2.18:
sinh(x) = x +
X3
X5
....
5!
- +-
3!
(2.18)
Eq. 2.17 can be simplified further if the electrical energy |ze4| is small compared to
the thermal energy kBT. In this case the first term in the sinh series is much larger
than the second term. As a result, all higher order terms can be ignored. With these
assumptions, eq. 2.17 can be linearized. The resulting equation, eq. 2.19, is known
as the Debye-Hiickel approximation:
V2
e
EOErkBT
2Vg,
(2.19)
where
]1/ 2 .
[e2nz2
EkBT
=
(2.20)
For a system with surface charge, eq. 2.19 has an additional term for the surface
charge density, p,(X, y, z). Eq. 2.21 is the modified equation [28]:
72=
(x, y, z)
+
2
(2.21)
The variable K is known as the Debye-Hiiekel parameter and plays a central role in
describing the strength of electrostatic interaction in colloidal systems. The extent of
the double layer is measured by ,-1, also known as Debye length, and ranges between
1 nm to 250 nm for most aqueous systems. At 25 'C in water, K-1 is given by eq.
2.22:
1
corR
-= (2
K
(
1
)1/2
-2000F2
0.304-
1
7 []m
[nm],
(2.22)
(2.23)
where I is the ionicity and F is Faraday's constant. The linearized PBE, eq. 2.19,
is valid for surface potentials where 0, < 25 mV. For a colloidal particle with
4,
>
25 mV, the non-linearized PBE, eq. 2.17, should be numerically solved, since the
linearized PBE is no longer valid at close proximity to the particle. However, for a
many-particle system where
@, >
25 mV, this becomes computationally prohibitive.
As a result, although solution of the linearized PBE may be less accurate, it continues
to be widely used in order to obtain behavioral trends and to identify regimes where
more detailed models may be required. Thus, larger phase-space can be analyzed by
compromising a bit on the accuracy of the solution.
Boundary Conditions and Interparticle Potential
Linearized PBE, eq. 2.21, is a second order equation. Therefore any mechanism to
obtain a solution requires two boundary conditions. One boundary condition is that
the gradient of Vb vanishes as r -+ oc:
V0 -iF/|r = 0
as
r - oo.
(2.24)
The limitations for the second boundary condition are: constant surface charge
or constant surface potential. It is instructive to consider the following scenarios
to infer the correct boundary condition. For an isolated particle, both boundary
conditions lead to an identical solution. The choice is more subtle when particles start
to interact. For like-charged particles with a constant charge boundary condition, the
electrostatic potential at the point of contact of particles would be close to twice the
surface potential of an isolated particle. On the other hand, for like-charged particles
with a constant potential boundary condition, close approach leads to an increase
of surface charge. Thus, although the results in these two regimes may be different
for like-charged particles, the physical behavior is similar: like-charged particles repel
each other. For oppositely charged particles with a constant potential boundary
condition, the surface charge would be infinity at the point of contact of particles.
Thus, oppositely charged particles would be inseparable on contact. In reality, this is
an incorrect assumption since each particle has limited charging sites, and therefore
the surface charge approaches a maximum as the particle separation becomes small.
As a result, one usually assumes a constant charge boundary condition for analyzing
colloidal interactions.
Choosing correct interparticle potential is also critical. There are two principal
potentials: the screened electrostatic Yukawa-type potential [47, 48] and the Ohshima
potential [49]. The Yukawa-type potential is valid at low ionic strengths. An important assumption for this potential is that the particle interior has properties (dielectric
constant and ionic strength) similar to the bulk solvent. Assuming that interactions
with neighboring particles can be neglected, the potentials can be superimposed. On
the other hand, the Ohshima potential assumes a Yukawa-type potential as the firstorder term and corrects for the ionic strength and dielectric constant of the particle
core by adding a series of converging infinite sums. However, in making these corrections, an additional assumption is made that two interacting particles are only
surrounded by the solvent. Thus, the Ohshima potential is not useful for low ionic
strength dispersions.
The interaction energy in the case of the Yukawa-type potential is given by a
product of the point-charge representation of one particle and the potential field of
other particles. The effective point-charge for a particle with radius, a, and surface
potential, V), is given by eq. 2.25 [50, 51]:
qpoit = 41reao, exp (n).
(2.25)
This is the result of superposition of the potential field of other particles and is known
as the linear superposition approximation (LSA). The total energy of interaction
between particles 1 and 2, with radii ai and a 2 , is given by eq. 2.26:
U1 2
=
(2.26)
qiq 2 exp( sr)
r
= [47rea1@s,1 exp (Kai)] [47rEa 2V8 ,2 exp (Ka 2 )]exp(-Kr)
(47re)
=
47reaia 2Os,1Vs, 2 exp (i(ai + a 2 ))
exp (-Kr)
r
r
(2.27)
(2.28)
The interaction potential in eq. 2.28 is called a Yukawa-type potential, or a screened
electrostatic potential [52]-[67]. It is widely used in this thesis to model the electrostatic interaction between particles.
Zeta Potential
Information regarding the interaction between particles depends on the electrical
double layer around them. Determining the zeta potential [26], (, for a colloidal
particle is a useful way of obtaining information about the structure of the double
layer. Electrokinetic processes are usually used to determine (. Electrokinetics refers
to processes in which the boundary layer between one charged phase and another
is forced to undergo some sort of shearing process. During this process the charge
associated with the particle's compact layer will move in one direction, and that
associated with the diffuse layer in the liquid, will move in the opposite direction. Zeta
potential is an electrokinetic potential, and is defined as the equilibrium potential at
the "surface of shear," where the velocity of liquid is zero.
Many electrokinetic processes can be used to determine (, although electrophoresis
is most widely used. When an electric field is applied to a particle, there is an external
force that moves the particle with a velocity that is proportional to (. Using a force
balance, eq. 2.29, one can obtain information about ( by measuring the terminal
velocity of the particle, v, which is related to the electrophoretic mobility, A,and the
applied electric field, E, by eq. 2.30:
F = -3v + Eq = 0
(2.29)
and
v
where
#
=
q
13
(2.30)
Ep,
1/s,.
Electrophoretic mobility for a particle can be related to ( through numerous methods. Two most common models are: the Hiickel model [68] (for na << 1) and the
Smoluchowski model [69) (for sa >> 1), where a is the radius of the particle.
The Hiickel regime is applicable when particles have a very thick double layer. In
this case, the electric field lines are unaffected by the particle, and the electrical force
on the particle is balanced by the viscous drag of the solvent. Thus:
o
47rE(a
=
E
67rqa
P= -
_
2f(
.
3q
(2.31)
The Smoluchowski regime is applicable when particles have a thin double layer.
In this case, the viscous force on the particle, on a volume element with surface area
A, is balanced by the electrical force. The viscous term is derived from the Stokes
equation and the electrostatic term is obtained from the Poisson equation. Thus, one
has:
d2 v
d20
dx 2 +EA+ dx 2 .
F
(2.32)
For the first integration, eq. 2.32 can be simplified by assuming that only velocity,
v, and electrical potential, 4, vary. As a result, eq. 2.32 becomes eq. 2.33:
dv
d
7-dx = -FE- dx + C
(2.33)
After integration of eq. 2.33, two boundary conditions are required in order to
obtain (.
These are: (i) electrical potential approaching zero, very far from the
particle and (ii) the velocity equal to zero at the surface of shear. With these, the
electrophoretic mobility is related to the zeta potential by eq. 2.34:
P=
.(
(2.34)
For most colloidal systems, it is easier to arrange for a > 1 than Ka < 1. Therefore, the Smoluchowski regime is more appropriate for colloidal systems than the
Hiickel regime.
2.2.3
Steric Interaction
In many colloidal systems, one adds non-ionic materials that adsorb on the surface of
the particles and prevent coagulation. In order to stabilize a colloidal system, these
molecules should not just adsorb onto the surface of particles, but also extend into the
solvent. The purpose of this morphology is to prevent particles from coming in such
close proximity, that aggregation may result. This is known as steric stabilization
while the interaction of polymer sheets as particles approach each other is called
steric interaction [31], [70]-[87].
The most notable steric stabilizers are non-ionic
block copolymers (BCP). One end of the BCP, usually lyophobic, adsorbs onto the
surface of the particle, whereas the other end, usually lyophilic, extends into the
solvent. Simple homopolymers are rarely used for this purpose, as they need to be
chemically grafted into the particle surface, if they are lyophilic. On the other hand,
if they are lyophobic, they would form a dense layer on the particle surface and will
be ineffective as stabilizers. Simple surfactant molecules also serve as good steric
stabilizers.
Most models that analyze steric interaction have two regimes. In the first regime,
when two sterically stabilized particles approach, the outermost parts of the surfactants start to mix. This results in increased enthalpy, as molecules prefer to be in the
solvent. This is called the osmotic regime, as the osmotic pressure of the solvent, in
the overlap zone, will be lower than in the bulk solvent. This leads to a driving force
for spontaneous flow of the solvent into the overlap zone, which pushes the particles
apart.
The second regime is when the separation between particles is less than the
length of one layer of surfactant. In this regime, the polymers (or surfactants) are
compressed. As a result, there are fewer possible configurations available for each
molecule. This leads to a reduction in entropy.
In order to analyze steric interaction, three pieces of information are required.
These are (i) the coverage of the polymer (in other words, the amount of polymer
adsorbed on a unit area of the particle surface); (ii) the thickness of the adsorbed
layer, once it extends into the solvent, and (iii) the profile of the outer part of the
layer.
2.2.4
Hydrophobic Interaction
Water molecules are known to form an extensive network of hydrogen bonds (Hbonds) with one another. When a non-polar substance is placed in water, water
molecules can reorient themselves around it without much loss of the hydrogen bonding. Reorientation is highly unfavorable entropically, as the molecules have fewer
available orientations. This is the reason why hydrocarbons are insoluble in water.
This effect on the H-bonding of water in the presence of non-polar substances, is
called the "hydrophobic effect." Closely tied to this is the hydrophobic interaction
[88]-[94].
For some time in the colloid community, it has been well known that hydrophobic particles placed in water attract each other over a distance of 10-30 nm, with
forces that are 10-100 times stronger than vdW force. However, no conclusive evidence exists about the origins of this force. First measurements of the hydrophobic
force were completed 27 years ago [92]. One source of confusion about the origin of
this force is the existence of two different force regimes. It has been suggested that
the measured hydrophobic force between particles is a combination of a short-range
(< 10 nm) truly hydrophobic force (that originates from the reorientation of water
molecules), and a long-range force (> 10 nm) due to a mechanism only indirectly
related to the hydrophobicity of the surfaces. Overcoming hydrophobic interaction,
either between particles or between a particle and a surface, is crucial in obtaining
higher mobilities of hydrophobic colloidal particles over surfaces. As will be shown
later (section 3.6), higher mobilities of colloidal particles are almost always required
for perfect 3D colloidal assembly.
2.3
Stability of Colloidal Dispersions: DLVO Theory
The stability of colloidal dispersions is dependent upon interactions that occur between particles and the solvent, as well as among particles. Collisions between particles that are suspended in a solvent are inevitable. If the particles are large, these can
be due to Brownian motion, agitation and flow, hydrodynamics or sedimentation. As
a result of these collisions, if the particles rebound off one another, the dispersion is
considered stable. On the other hand, if the particles coagulate as a result of collisions
the dispersion is considered unstable.
The stability of monodisperse spherical colloids is often described by the "Derjaguin [95], Landau, Verwey and Overbeek [96]" (DLVO) theory. In this theory, the
stability of the colloidal dispersion is interpreted as a change in energy, resulting from
the effects of colloidal forces, as two particles approach each other. The total energy
is given by eq. 2.35:
UDLVO
=
Ueiectrostatic +
UdW.
(2.35)
For most aqueous dispersions of monodisperse particles, at an interparticle separation
of 100 nm or more, vdW and electrostatic interactions have no effect on particles.
When the particles approach one another, there is an increase in the electrostatic
as well as vdW interaction. As the vdW force increases faster than the electrostatic
force, there is a slight domination of the vdW force resulting in a weak secondary
minimum. As the interparticle separation decreases further, the repulsive electrostatic
interaction leads to a barrier that prevents particles from coming closer. This occurs
until a critical distance is reached, at which the vdW force dominates the electrostatic
force, resulting in strong irreversible coagulation. The behavior of particles on close
approach is also dictated by their kinetic energy. If the kinetic energy of colliding
particles is large enough to surmount the barrier, coagulation in the primary minimum
will result. If the particles do not have enough kinetic energy, then stable weak particle
associations result in the secondary minimum. The depth of the secondary minimum
depends on the Hamaker constant and particle characteristics such as surface charge
density, particle radius, etc.
2.4
Self-assembly of Colloids
Self-assembly is defined as the spontaneous organization of two or more components
into larger aggregates using covalent or non-covalent bonds. It is a bottom-up approach that relies on the cooperative interactions of small components. The components assemble spontaneously to produce larger structures in two or three dimensions
[97].
This section describes two types of self-assembly of colloidal particles: (i) nontemplated self-assembly, where the individual particles interact to produce a larger
structure without the influence of external forces or spatial constraints and (ii) templated self-assembly, where the individual particles interact with each other and an
external force or a spatial constraint to produce a larger structure. More detailed
discussion on other aspects of self-assembly can be obtained elsewhere [98].
Figure 2-1: SEM image of the top view and cross-section of a colloidal crystal of
polystyrene particles. The particles assemble in a face centered cubic (f.c.c.) structure
with (111) orientation relative to the substrate.
In a dispersion of charged monodisperse particles with radius R, three-dimensional
organization of particles into close-packed structures, such as face centered cubic
(f.c.c.), takes place at low KR. More complexity can be added by using a binary
system- in other words, a dispersion with two types of particles. A beautiful example
of this phenomenon is the formation of Ionic colloidal crystals (ICCs) [23], [99, 100,
101]. ICCs are crystals that form in a dispersion with two particle types, such that
the particles are oppositely charged. They are formed at large Debye lengths (>100
nm). This concept was proposed by Dr. Garry Maskaly [101] and experimentally
demonstrated by Leunissen et al.
[23].
Since these structures are formed in the
solvent, solvent behavior plays a central role in their formation. As a result, ICCs
can be easily destroyed on exposure to atmosphere (this leads to an increase in KR) or
vibrations. Thus, the majority of methods are based on obtaining colloidal crystals
without the solvent (made solely of colloidal particles). These structures are known
as colloidal crystals.
The easiest way to obtain a colloidal crystal is by drying a dispersion of monodisperse colloids. As the solvent evaporates, capillary forces pack the particles into a
close-packed structure [102]. A scanning electron microscope (SEM) image of this
structure is shown in fig. 2-1. Amid a self-assembly process, there are only a few
parameters that can be controlled to influence the final structure. Chief among these
are the concentration of the dispersion, Debye length and density of the solvent.
If there were no interactions between particles in a dispersion, on collision they
would behave like billiard balls. This type of interaction is called a hard-sphere
interaction [103]. However, if the particles are charged, they interact mainly through
electrostatic and vdW interactions. Hence, they behave as soft spheres because their
"presence" is felt by other spheres in the suspension. Hard-sphere suspensions act
like fluids at low volume fraction of particles, #, but crystallize into a close-packed
structure when
#>
0.55. On the other hand, suspensions of charged particles form
close-packed f.c.c. with (111) orientation (relative to the substrate at
By lowering
# further,
#>
0.10 [104].
one can obtain a structure with body centered cubic (b.c.c.)
packing. Detailed studies have been done on the phase behavior of colloids and can
be explained by a pure Yukawa or a hard-sphere plus Yukawa-type potential.
In order to assemble more complex structures with different orientations, newer
periodic potentials should be created. These potentials need to be anisotropic so that
they break the isotropic symmetry of the colloidal interactions that results in f.c.c.
crystals with (111) orientation. Such potentials have been created by applying external electric or optical fields and by manipulating the interaction potentials. Crystal
orientation can also be controlled by using a patterned surface. Periodic one- or
two-dimensional height profiles impose uniformly varying potentials on the colloidal
spheres, during their assembly. Van Blaaderen et al. [105] were among the first to
explore this idea. In the following subsections, processes used for self-assembly of
colloids are discussed.
2.4.1
Methods of Self-assembly
Colloidal assembly can be induced by gravitational [106, 107, 108], electric [109]-[112]
and magnetic fields [113, 114]. Although sedimentation is conceptually easy to understand, precise control of parameters, such as size and density of the particles, is
needed to obtain a large single crystal. Particles will only settle, in times that are
short enough to be observed, if their size and density are large enough. Controlled
sedimentation of particles in a gravitational field leads to a f.c.c. crystal. Unfortunately, the process of sedimentation is rather slow, and successful fabrication of a
crystal can take weeks. The sedimentation can be expedited through centrifugation
or filtration [115]. Although these processes are faster, the quality of the crystals
shows negligible improvement.
Another disadvantage of the gravity method is that the thickness of the colloidal
crystal cannot be controlled during sedimentation. In comparison, vertical deposition
techniques [116]-[122] are ideal for controlling the thickness of the colloidal crystal.
During vertical deposition, a substrate is held vertically in a beaker that has a colloidal
dispersion. Colloids assemble on the substrate either when the substrate is pulled out
slowly, or when the suspension is evaporated or pumped out slowly. Convective
assembly is one of the most widely used vertical deposition method [117]. Convective
assembly has often been used to make 2D colloidal crystals (or, in other words,
colloidal monolayers). During convective assembly, crystallization is initiated in the
solvent meniscus by attractive capillary forces between the particles at the drying
front. These capillary forces lead to particle aggregation. A schematic showing the
shape of a meniscus and arrangement of particles on the substrate is shown in fig.
2-2.
A balance between convection and capillary forces is essential for the formation of
a uniform monolayer. A few recent reports [2, 21] use one or another form of vertical
deposition to obtain a particle monolayer. The formation of two-layer binary colloidal
crystal was also first reported using vertical deposition [123]. For this process, a closepacked layer of large particles is first formed through convective assembly. In the
second step, depending on the concentration of smaller particles in the dispersion,
some or all of the interstices in the first layer are filled. In order to have precise
control of thickness, domain size and ordering in the crystal, a number of parameters
need to be carefully controlled simultaneously. These include the choice of substrate
material, tilt angle of the substrate with respect to the liquid-air interface, solvent,
ambient temperature, relative humidity, concentration of colloids and evaporation
.1.....
....
..
...
. ....
................................
...........
Substrate
of the suspension
Capillary Forces
0
Figure 2-2: Schematic of a convective assembly process.
rate. Fabrication of large photonic devices demands large ordered domains. As shown
by Xia et al. [124], using physical confinement of colloidal particles leads to colloidal
crystals, with different orientation and larger ordered domains, compared to crystals
created on bare substrates.
2.4.2
Directed Self-assembly
Using bare templates makes it difficult to control the orientation of colloidal crystals.
Templated assembly allows for the fabrication of crystals with predefined orientation.
In-depth discussion of the progress in templated assembly of colloids is available
elsewhere [125]-[129].
Templates can be created by physical patterning [130]-[133] (known as hard lithography) or by chemical patterning [134]-[138].
Chemical patterning methods, like
soft lithography and nanoimprint lithography, are widely used to print and attach
molecules on the surface of a substrate. The topological pattern of the stamp determines the chemical pattern on the substrate. Colloids can be assembled on these
chemically patterned regions of the template by vertical deposition methods. Another
widely used method is dip-coating. In dip-coating, chemically patterned substrates
are dipped, held and then withdrawn from a colloidal dispersion [139]-[144]. Chemical patterns can lead to either positive or negative patterns of particles. In positive
patterns, particles assemble only in regions that are chemically stamped, whereas in
negative patterns they assemble only in regions without the chemical stamp. Colloidal assembly on chemically patterned templates occurs because of a combination
of electrostatic and hydrophobic interaction between the chemical pattern and the
particles and capillary interaction between colloidal spheres.
Assembly on Templates created by Lithography
Although chemically patterned templates are easier to make, physically patterned
templates offer better control of the orientation of assembled structures. Van Blaaderen
et al. [105] were the first to demonstrate the use of a patterned template to obtain a
colloidal crystal with a known crystallographic orientation. Morphological patterning
of substrates has been successfully used to direct crystallization in the semiconductor
industry as well as in block copolymer ordering. Standard approaches used to create
these, are electron beam lithography and interference lithography.
One of the simplest topographical templates consists of periodic grooves with a
rectangular shape. Whitesides et al. [145] studied the coupling of laminar flow of
colloidal dispersions with topological confinement of particles in the groove. They
showed the formation of close-packed hexagonal, rhombic or disordered structures
depending upon the ratio of the particle diameter to the width of the groove. More recently, Ozin et al. [146] used templates with tapered dimensions to fabricate colloidal
crystals with (100) orientation relative to the substrate. They created anisotropically
etched, V-shaped grooves inside Si(100) wafers through lithography. Subsequently,
colloidal particles were sucked into these grooves by capillary forces during convective
assembly. Colloidal crystals with multiple layers formed as a result. Following the
same approach, Yodh et al. [147], achieved well-ordered and defect-free f.c.c. colloidal
crystals (up to 50 layers) by using a template with a square pattern.
As a nice continuation of the above approach, Xia et al. [148, 149] used a template
with etched 2D regular arrays of pyramidal tips in Si. The objective was to obtain
a f.c.c. colloidal crystal with an orientation different from (111). They were able to
obtain f.c.c. crystals with (100) orientation. Matuso et al. [150] demonstrated that
by varying the opening angle of the pyramids through lithography, one can control
the orientation of the assembled crystal. They obtained f.c.c. colloidal crystals with
(100) as well as with (110) orientations. In another work, Xia et al. [129] created
colloidal particle aggregates with many shapes such as dimers, triangles, pentagons
and hexagons. For this work, they used a template with holes patterned in (110)
symmetry. Thereafter, by varying the ratio of the particle diameter to the hole
diameter, they were able to create differently shaped aggregates.
Binary colloidal crystals exhibiting building blocks of different sizes were fabricated using a layer-by-layer method by van Blaaderen et al. [123]. The authors prepared a hexagonally close-packed layer of large particles using convective assembly.
In the second layer, smaller like-charged particles were directed into the interstices of
the first layer, also using convective assembly. The array of arrangements included
AB, AB 2 and AB 3 , depending upon the concentration of smaller particles that were
used for deposition. More recently, Wang et al. [151] have shown that spin-coating
of particles can be used to prepare the second layer. In this method, spin speed determines the final structure. At lower speeds the authors obtained AB 2 order, and at
higher speeds, AB 3 order.
Templated self-assembly was originally conceived as a promising route to fabricate
complete photonic band gap (CPBG) structures. Colloids are of interest as CPBG
building blocks because, by changing the size of the constituent particles, the band
gap can be shifted. Although the results outlined in this section are useful, they fail to
offer a clear procedure for making CPBG structures. Recently, Santamaria et al. [14]
fabricated the diamond cubic structure by using a prefabricated template (with holes
arranged in a square pattern), silica and polystyrene (PS) particles. This method is
an excellent example of templated assembly.
Chapter 3
Controlled Ordering of Oppositely
Charged Colloidal Particles
3.1
Introduction
Ordered crystalline packing of nanoscale particles have technological applications,
including those in photonic materials [11, 12, 13], sensing [6, 7, 8] and molecular filters [9, 10]. Ordering in colloidal suspensions, which is a well-known phenomenon,
provides a template for ordered nanoscaled structures, if the suspending media can
be removed without disrupting particle ordering [152]. Conventional processes for
ordering colloids, which employ repulsive forces between particles that carry electrostatic charges of the same sign, produce close-packed crystalline analogs. Using a
composite suspension of two particle types, each monodisperse with a different size
and with opposing charge, provides a method to create colloidal crystals of lower
symmetry [23, 101, 153], and therefore may produce stable structures with novel photonic, sensing, and filtering properties. However, processing methods that produce
lower symmetry structures prove to be more difficult to realize, primarily because the
colloidal composites attractive electrostatic and vdW forces limits the length scale of
ordering.
Researchers have shown that a suspension with oppositely charged particles can
have long-range order if the particles are weakly charged and sterically stabilized
[23]. Additionally, the Debye length needs to be on the scale of particle diameter
and the vdW forces need to be absent. As a result, although the particles can stay
ordered (in the solvent), the stabilizing forces are mild. Therefore the structure can
be destroyed on exposure to atmosphere or vibrations, or when the solvent is removed. Such a system has limited applicability. Recently, Mukhopadhaya et al. [154]
showed that strongly and oppositely charged PS particles can order irrespective of
their surface charge. Neither did they disclose the Debye length in the system from
which these structures were crystallized, nor did they elaborate on the stabilizing
forces and mechanism. Their results are contrary to the available literature about
oppositely charged particles. For instance, a simple experiment shows that when
positively charged PS particles are distributed onto a layer of negatively charged PS
particles, attractive electrostatic forces are so strong that they trap the particles in a
deep primary minimum. The resulting structure has no long-range order. Therefore,
in the absence of a clear explanation it becomes imperative to understand the mechanism for ordering oppositely charged colloids. Factors that influence the assembly
of oppositely charged particles into ordered structures can then be exploited to make
three dimensional structures that remain ordered as the solvent dries.
Ordered aggregates of oppositely charged particles show greater stability compared to their like-charged counterparts. Therefore, they are better candidates for
making low-volume non-close-packed structures. Whereas the like-charged analogs
are stabilized by vdW forces only, the oppositely charged non-close-packed structures
are stabilized by vdW as well as electrostatic forces.
A layer-by-layer method is reported herein [22], and demonstrates a simple processing route for making 2D low-symmetry packing of strongly and oppositely charged
colloids. Previous observations [23] demonstrate that sterically stabilized, weakly and
oppositely charged colloidal particles can produce low-symmetry ordering in suspensions. However, these colloidal crystals are stable when in suspension and for weakly
charged particles. Schevchenko [155] on the other hand, has shown that it is possible
to evaporate the solvent and retain order for smaller, weakly charged nanoparticles.
Three studies are discussed in this chapter. In the first study, spin-coating is
used to distribute charge-stabilized colloids [151] on an underlying layer of larger and
oppositely charged colloidal particles. It is demonstrated that a surface agent, which
produces short-range steric repulsion, permits ordering even as the particles' opposing
charges are increased to magnitudes that prevent ordering in previous observations.
In the second study, it is shown that, by manipulating the electrostatic repulsion
between like-charged particles, a non-close-packed layer of particles can be assembled
on a layer of close-packed and oppositely charged particles. Since capillary attraction
between particles can lead to close-packed structures, schemes that rely on rapid
assembly through evaporation of the solvent cannot be used here. As a result, dipcoating is used to distribute and arrange particles in the second layer.
In the third study [156], ordering of hydrophobic, charged particles on charged
surfaces is discussed. It is shown that amphiphilic surfactants can be used to order
hydrophobic particles on hydrophobic, like-charged surfaces.
3.2
3.2.1
Materials and Methods
Colloidal suspensions
Suspensions of monodisperse polystyrene (PS) beads measuring 100 nm (amidine
functionalized, (= 52.56 mV at i-1= 127 nm, and charge density measured by the
manufacturer equal to 0.032 C/m 2 ) 210 nm (amidine functionalized, (= 54.62 mV at
-1 =
127 nm, and charge density measured by the manufacturer equal to 0.1 C/m 2 )
and 420 nm (sulphate functionalized, (= -61.57 mV at K-1= 127 nm, and charge
2
density measured by the manufacturer equal to -0.032 C/m ) were purchased from
Molecular Probes Inc., Eugene, OR. Electrophoretic mobility for different colloidal
samples was measured using a Zeta-PALS (Brookhaven Instruments Corporation).
Once electrophoretic mobility was measured, zeta potential was calculated using the
Smoluchowski model. The PS suspensions were dialyzed against DI water to lower
their salt concentrations before use.
3.2.2
Surfactants
Triton-X 100 ((C1 4 H22 O(C2 H4 0),) was purchased from VWR International Inc. In
most cases 60-70 pl of 10 w/v% Triton X-100 was added to 1 ml of the final suspension
of colloidal particles before spin-coating. Adsorption of the non-ionic surfactant on
PS was measured by Quartz Crystal Microbalance (QCM-D E4 from Q-Sense AB,
Sweden). A single sensor crystal with PS spin-coated on gold, which was purchased
from Q-Sense, was used for all the experiments. QCM can measure the change in
the resonance frequency depending on the change in mass of the sensor crystal, i.e.
if anything is adsorbed or desorbed from the sensor crystal. The change in frequency
can be related to the change in mass by the Sauerbrey equation (eq. 3.1).
Am = -C
where
Am
n
,
(3.1)
is the change in mass and Af is the corresponding change in resonance
frequency. C is 17.7 ng cr-2Hz-1 and denotes a constant that characterizes the
sensitivity of the equipment to the change in mass and n is the resonance overtone.
For all the measurements described in this study, the third overtone (n=3) was used at
a temperature of 25'C. The fundamental resonance frequency for the sensor crystal
was 4.95 Mhz. The sensor crystal was cleaned with copious amount of de-ionized
(DI) water prior to any measurement. Thereafter, it was placed in the QCM cell
where a baseline measurement was done in DI water. This was followed by QCM
measurements in Triton-X 100 suspensions in DI water. Five suspensions of Triton-X
100 in DI water were used in this study. They were 0.01cmc, 0.1cmc, cmc, 5cmc
and 10cmc, where cmc is the critical micelle concentration for Triton-X 100 (cmc
for Triton-X 100 in water is 0.24 mM [157]). Between any two measurements, the
adsorbed surfactant was washed off the sensor crystal by running DI water through
the cell. A flow rate of 0.5 ml/min was maintained during all the QCM measurements.
Cationic Polyelectrolyte Dodecyltrimethylammonium bromide (DTAB, CH3
(CH 2)11 - N+ - (CH 3 ) 3 - Br-) has a cmc of 15.6 mM/l (i.e., 4.810 mg/ml).
-
It
dissociates in aqueous solution with a positively charged headgroup. The concentra-
tions used in this study ranged from 0 to 4 mg/ml. Block copolymer (BCP) Poly(Nmethyl 2-vinyl pyridinium iodide-b-ethylene oxide) (P2VPQ-PEO) was bought from
Polymer Source Inc. Between 0-0.5 M of this amphiphilic and cationic BCP, was used
in experiments.
3.2.3
Solvents
De-ionized water (DI water) was used for most of the experiments and was readily
available. However, in one case, Class 1 isopropanol (Hubbard Hall Inc.) 80%-DI
water 20% mixture, was used. The Debye screening length for DI water with varying
salt concentrations was calculated based on conductivity measurements (YSI 3200
Conductivity Instrument).
3.2.4
Template
Interference Lithography
Interference lithography (IL) provides an easy and simple way to create periodic
patterns on a substrate. With a single exposure, pattern of gratings with periods as
small as 170 nm can be written. More complex patterns, like grids, holes or poles can
be written with multiple exposures.
The basic principle of interference lithography (IL) is as follows: two mutually
coherent beams of light intersect and form a standing wave in the region where these
two overlap. Fig. 3-1 shows the set-up for an IL system. For this thesis, Lloyd's mirror IL was used. In a Lloyd's mirror IL set-up, spatial as well as temporal coherence
is important to consider. Temporal coherence defines the narrowness of the range of
wavelengths from a light source. For IL, the important measure of temporal coherence is coherence length. This defines the maximum distance along the direction of
propagation of the light wave, over which, waves can be expected to show mutual coherence. If light waves come from different sources, they would be incoherent. Thus,
a single light source is used to promote mutual coherence. In a Lloyd's mirror set-up,
the mirror divides a wavefront from the source into two overlapping beams that form
.............
. I .. - .... .
..........
....
......
....
V
.
_,W
-
11,-
- -
........................
Figure 3-1: A schematic for the Lloyd's Mirror Interference Lithography set-up
the interference pattern. In order to form a fringe pattern with good contrast, the
path lengths of the two interfering beams from the source to a point on the substrate
should differ by less than the coherence length. In the current set-up, the light comes
from a helium-cadmium (HeCd) laser, emitting at 325 nm. The particular model of
laser used in the Lloyds mirror has good temporal coherence, with a coherence length
of 30 cm, long enough that temporal coherence is generally not a concern.
Spatial coherence defines the uniformity of the wavefronts along the width of the
beam. For instance, if a source has good spatial resolution, it will appear like a point
in space and the wavefronts will appear as concentric spheres centered on a point. In
the Lloyd's mirror set-up, the light is spatially filtered before reaching the substrate.
Practically, the beam should expand to cover the exposure area with high intensity
and uniformity. This is achieved by using a lens to focus the beam through a 5 Im
pinhole. Since there are no collimating optics between the pinhole and the substrate,
the beam expands to a diameter of about 30 cm at the wafer chuck. As the spatial
filter is the last element before the light reaches the substrate, the wavefronts reaching
::::::= :::::::
......................
..'Zz.
.zzmmmmmu:
IIIIIIII- IIIIIIII.m.:::::..:W
...........
.....
................
the substrate are nearly spherical.
Template preparation
Silicon templates were prepared through IL. A 4-inch silicon wafer was spin coated
with negative photoresist PS4. After baking, this was exposed to a 325 nm wavelength, HeCd laser. A pattern of holes arranged in (110) symmetry was created as
follows. The baked wafer was exposed in IL for 33 seconds at 0.23 mW. It was then
rotated 90 degrees and exposed again for 33 seconds at 0.23 mW. The resulting pattern was baked for 90 seconds at 110 *C and then developed in CD-26 developer for
60 seconds. This creates a pattern of holes with (110) symmetry in the photoresist.
-
To etch the pattern of holes into silicon, the sample is treated in a plasma-etcher
with CF4
02
plasma at 20 mTorr for 3 minutes. In the end, the photoresist is re-
moved by treating in 02 plasma at 20 mTorr for 7 minutes. A schematic for template
preparation is shown in fig. 3-2.
1
Coating of
Spin
the Photoresist
2. Exposure
3. Development
/N/VVV\Ik/
4 RIE with CF4
SILICON
5. Photoresist Removal
PHOTORESIST
Figure 3-2: A schematic for the procedure to fabricate the template
.
3.2.5
Spin-coating
Glass substrates to be used, were cleaned by ultrasonication in acetone followed by
treatment in Pirhana solution, which is a mixture of concentrated sulfuric acid (VWR
international Inc.) and hydrogen peroxide (Alfa Aesar) (H2 SO4 : H2 0 2 = 3:1, volume
ratio) to obtain a hydrophilic surface. It was then washed with copious amounts
of water and dried with nitrogen gas before use. The first layer from negatively
charged PS particles was made by convective self-assembly. In this method the clean
micro glass plate was fixed vertically inside a beaker, which contained the colloidal
suspension at 35'C as the suspension is slowly pumped out of the beaker forcing the
particles to pack under the capillary forces.
Spin-coating was used to distribute the positive PS particles on the substrate made
from negative PS particles. Spin-coating has been previously used to make charge
stabilized 2D colloidal crystals [151].
Starting with 50pl of the dialyzed colloidal
solution with manufacturer supplied concentrations (provided above), 0.25-w/v% and
1.0 w/v% suspensions of 100nm positive PS particles were prepared for spin-coating
in DI water whereas 1.0-w/v% solution of 210 nm positive PS particles was prepared
in DI water. In most cases 60-70 pl of 10-w/v% Triton X-100 was added to the final
solution before spin-coating. Spin-coating was done at 3000 rpm for 60 seconds for
all of the above systems by putting approximately 20 pI of the resulting solution,
on a substrate of negatively charged 420 nm PS particles. Additionally, for 0.25w/v% solution of 100nm positive PS particles, spin-coating at 3000 rpm was done
with 0.01635 mM, 0.094 mM and 0.879 mM NaCl salt concentrations. Table 3.1
lists the Debye lengths that are inferred from conductivity measurements on solvents
without addition of any colloidal particles to the solvent, for the above three salt
concentrations and a measurement with no added salt (DI water). Calculations show
that on addition of colloidal particles, the change in Debye length, due to the counterions from charged particles is not substantial. Therefore, the Debye lengths calculated
[158] for solvents without addition of particles were used for all calculations in this
work. For 1-w/v% solution of 100 nm positive PS particles, spin coating at 6000 rpm
for 60 seconds was also done. Finally, the spin-coated substrates were sputtered with
gold for 20 seconds before being imaged under the Scanning Electron Microscope
(SEM) (Gemini 982, Zeiss).
Table 3.1: Variation of Debye length with increasing NaCl concentration in water
NaCl concentration [ x 0.01 mM]
No added salt (DI water)
1.635
9.4672
87.9
3.2.6
Debye screening length [nm]
250.354
75.22
31.26
10.256
Dip-coating
Dip-coating was used to form a non-close-packed layer of colloidal particles on an
underlying layer of oppositely charged particles. The substrate was a close-packed
layer of 420 nm negatively charged spheres. Before dip-coating the substrate, it was
made hydrophilic by exposure to oxygen plasma for 10 seconds. This is required for
obtaining a monolayer of particles in subsequent deposition steps. Thereafter, it was
dipped in a 0.1-w/v% suspension of 140 nm positively charged PS particles for 60
seconds. In order to reduce irreversible coagulation of oppositely charged colloidal
particles due to electrostatic attraction, Triton-X 100 was added to the suspension
of positively charged particles. By lowering the surface tension of water, Triton-X
100 also reduces capillary attraction between positive PS particles. To further limit
the close-packing of positive PS spheres, the substrate is slowly withdrawn, manually,
from the suspension of colloids and immersed in DI water without drying. It is allowed
to stay in water for about 60 seconds, after which it is dried at ambient temperature
(250 C).
Figure 3-3: SEM image of 100 nm diameter positively charged PS sphere suspension
(0.25-w/v%) spin-coated at 3000 rpm on a substrate made from 420 nm diameter
negatively charged PS spheres
Figure 3-4: 100 nm diameter positively charged PS sphere suspension (1.0-w/v%)
spin-coated at 3000 rpm on a substrate made from 420 nm diameter negatively
charged PS spheres
3.3
Spin-coating of Oppositely Charged Colloids
Fig. 3-3 and fig. 3-4 are SEM images for 100 nm positively charged polystyrene (PS)
particles suspended in DI water and spin-coated on a hexagonally ordered packing
made from 420 nm negatively charged PS particles. These figures indicate that some
short-range order may be present but long-range ordering is not produced by spincoating positive PS particles on the negatively charged substrate of PS particles when
no surfactant is added. While not representative of most of the system, the shortrange order (enclosed within the box in fig. 3-3) showing a 100 nm positive PS sphere
separated from the other three 100 nm (= D) diameter spheres by a distance h (= r
- R1 - R 2 ) of 193.97 nm (~~2D), is produced by electrostatic repulsion between the
positively charged PS spheres since the Debye length in the present case is on the order
of the interstitial spacing ( 250.5 nm ~ 2.5D). The absence of long-range order in fig.
3-3 and fig. 3-4 can be attributed to the strong DLVO attraction between oppositely
charged PS particles. Besides the strong electrostatic attraction between oppositely
charged colloids, the hydrophobic interaction between PS spheres also reduces the
mobility of positive PS spheres, being spin-coated. However, as discussed in section
3.5, introduction of a short-range repulsive interaction, in the form of a steric barrier
can lead to ordered assemblies.
3.3.1
Surfactantless spin-coating of colloidal particles
In the absence of a non-ionic surfactant, electrostatic and vdW attraction prevent ordering of the spin-coated oppositely charged colloidal spheres whereas the hydrophobic interaction between the positive and negative PS spheres reduces their mobility.
Spin-coating positive PS spheres from a suspension with reduced electrostatic
interaction (in other words by increasing the salt concentration) leads to lower electrostatic attraction between oppositely charged colloidal spheres. The increased salt
concentration concomitantly reduces the electrostatic repulsion between positively
charged PS spheres, resulting in their coagulation during spin-coating. Additionally,
hydrophobic interaction between the positive and negative PS spheres still prevents
greater mobility of the spin-coated PS spheres. In order to improve the mobility of
the spin-coated positive PS spheres the solvent was changed from DI water to an
isopropanol(80%)-DI Water(20%) mixture. Isopropanol wets PS better than water
and therefore leads to greater mobility of the particles being spin-coated on the substrate. Additionally, isopropanol has a lower surface tension than water and exerts
a weaker capillary force than water. This can lead to fewer coagulates. Not surprisingly, DI water-IPA suspension of 100 nm negatively charged PS particles when
spin-coated onto a substrate made from 420 nm negatively charged PS leads to an
ordered packing. However, on spin-coating positively charged PS particles suspended
in a mixture of isopropanol and DI water, there are a number of coagulates as well
as a disordered structure as shown in fig. 3-5. Isopropanol has a relative permittivity
(e20) nearly a fourth that of water (~80. 1) and therefore a Debye length which is half
that of water under identical salt concentrations. The coagulation in the presence of
isopropanol can therefore be explained based on reduced Debye length. Moreover on
using 80%-20% mixture of isopropanol- DI water, although leading to greater mobility
for spin-coated positive PS spheres, is not sufficient to offset the strong electrostatic
and vdW attractive forces. This leads to the disordered packing observed in fig. 3-5.
3.3.2
Spin-coating of colloidal particles with non-ionic surfactant
Long-range and well ordered regions of oppositely charged colloidal particles are observed on spin-coating positive PS sphere suspension with a non-ionic surfactant
(Triton X-100 (C1 4H22 O(C 2 H4 0), with n 9 - 10) [159, 160] on the substrate made
from negative PS spheres (fig. 3-6), where the hydrophobic end of the surfactant adsorbs to the PS surface; the other end is hydrophilic and soluble in water. Adsorption
of the non-ionic surfactant on the positive PS particle surface leads to a steric barrier,
which serves as a short-range repulsive force. Because this surfactant is non-ionic, it
has no effect on the total surface charge and prevents particle coagulation whereas
Figure 3-5: 100 nm diameter positively charged PS sphere suspension (1.0-w/v%) in
isopropanol (80%) - DI water (20%) spin-coated at 3000 rpm on a substrate made
from 420 nm diameter negatively charged PS spheres
the amphiphilic character of it produces a change in the hydrophobicity of PS. As
shown in section 3.5, this promotes particle rearrangement into lower energy configurations during spin-coating. Other non-ionic, amphiphilic surfactants may produce
long-range ordering as well. Spin-coating from a 0.25-w/v% suspension of positively
charged PS particles in water at 3000 rpm, with Triton-X 100 in the suspension,
produces the 2D LS 2 ordered structure shown in fig. 3-6 (size ratio of 4.2). The LS 2
structure remains stable up to a particle size ratio of 2 (210nm positive PS on 420 nm
negative PS) (fig. 3-8). On doubling the rotation rate of the spin-coater to 6000 rpm
and increasing the concentration of 100nm positive PS particles in the suspension
to 1.0-w/v%, a LS 6 long-range ordering is present (fig. 3-10). Ordered regions were
typically 200-400 pm 2 large, as shown in fig. 3-12 and fig. 3-13.
Combining rapid
ordering of oppositely charged colloids through spin-coating with templated assembly, one can fabricate binary colloidal crystals with a non close packed orientation.
By using a template, a layer of 250 nm negatively charged PS particles were ordered
with (110) orientation, through convective assembly. In the second step, spin-coating
was used to spread 20-40 pl of a 1.5-w/v% suspension of 140 nm positively charged
...........
.......
-
.........
.
Figure 3-6: 100 nm diameter positively charged PS sphere suspension (0.25-w/v%)
in DI water with Triton X-100, spin-coated at 3000 rpm on a substrate made from
420 nm diameter negatively charged PS spheres for 60 seconds
3-
2
g(r)
I....
5
10
15
rio
2
I
25
.1
30
Figure 3-7: Pair distribution function (pdf) for small particles from fig. 3-6, a is the
diameter of the small sphere
.....
........
...........
. ......
....................
. .....
Figure 3-8: 210 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in DI water, spin-coated at 3000 rpm on a substrate made from 420 nm diameter
negatively charged PS spheres for 60 seconds
3
2.5
2
1.5-
g(r)
0.5
0
.
2
4
8
8
_
.
.
.
10
.
.
.
.
12
.
.
a
14
.
.
.
a
16
.
.
.
a
18
rio
Figure 3-9: Pair distribution function (pdf) for small particles from fig. 3-8, a is the
diameter of the small sphere
.......
.........
......
.....
Figure 3-10: 100 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in DI water, spin-coated at 6000 rpm on a substrate made from 420 nm diameter
negatively charged PS spheres for 60 seconds
6
5
4
3
g(r)
2
1
0
, ,.
.
0
I
5
.
.
.
.
I
10
.
I
.
I .
15
.
.
I
20
I
.
.
I
I
,
.
25
ria
Figure 3-11: Pair distribution function (pdf) for small particles from fig. 3-10, a is
the diameter of the small sphere
Figure 3-12: SEM image of a larger domain with LS 6 ordering
PS particles on the substrate at 3000 rpm. The resulting structure has CsC1 symmetry. Fig. 3-14 shows a SEM micrograph where the first layer of 250 nm negative PS
particles and the second layer of 210 nm positive PS particles are seen.
3.4
Dip-Coating of Oppositely Charged Colloids
The zinc blende or the ZnS structure has been reported to have a complete photonic
band gap (CPBG) [12] with a large enough dielectric contrast. Indeed, by merely
scaling the size of the colloidal constituents in this structure, the frequencies that are
blocked can be changed. Along the (111) plane, ZnS presents a unique configuration
in which only one type of charged species constitutes a layer. The assembly of ZnS
type structure was attempted through the following procedure: the starting substrate
should have f.c.c. symmetry with (111) orientation and it should be made of likecharged (negative) colloids. The second layer of particles should be oppositely charged
and smaller. These should fill only half of the interstices on the first layer. The final
structure is akin to the schematic shown in fig. 3-15. The third layer of negatively
charged colloids then sits on top of the positive ones. Fig. 3-16 shows the most
Figure 3-13: SEM image of a larger domain with LS 2 ordering
Figure 3-14: 140 nm diameter positively charged PS sphere suspension (1.0-w/v%)
in DI water, spin-coated at 3000 rpm on a substrate made from 250 nm diameter
negatively charged PS spheres for 60 seconds. The layer of 250 nm particles were
assembled on a template with holes arranged in (100) symmetry, through convective
assembly.
.....
..........
.... ......
... .....
....
.
.....
..
......
.................
- ""
.................
....
........
..
..
. ...............
energetically favorable positions for negative PS particles in the third layer. The
most energetically favorable positions for positive particles in the fourth layer are
shown in fig. 3-17.
Os
Figure 3-15: A schematic showing the first two layers for a layer-by-layer assembly of
ZnS-type structure. Green spheres represent positive PS particles in the second layer
and red spheres represent negative PS particles from the first layer. In the second
layer only half of the total interstices are occupied.
Fig. 3-18 is a SEM micrograph of a non-close-packed layer of 140 nm positive
PS particles arranged on top of a close-packed layer of 420 nm negative PS particles.
The first layer of negative particles was deposited using convective transport from a
suspension of 420 nm PS particles. For the second layer, adsorption seems to be the
most appropriate method. The parameter that determines the ordering in the second
layer is the Debye screening length in the suspension of positive PS particles. Since
the particles are oppositely charged, the amount of contact between the negatively
charged substrate and the suspension of positively charged particles is critical. As a
result, convective assembly cannot be used to deposit particles in the second layer.
Although an assembly of particles through dip-coating is less uniform, limited time
of contact between oppositely charged particles is a more important factor.
Figure 3-16: A schematic showing the first three layers for the layer-by-layer assembly of ZnS-type structure. Green spheres represent positive PS particles in the
second layer and red spheres represent negative PS particles. The position of negative
particles in the third layer is shown in translucent blue.
Figure 3-17: A schematic showing the first four layers for a layer-by-layer assembly of
ZnS-type structure. Green spheres represent positive PS particles in the fourth layer
and red spheres represent negative PS particles
. .. ....
..
...............................
-
Figure 3-18: SEM image after a suspension of 0.1-w/v% 140 nm diameter positively
charged amidine functionalized PS spheres with Triton X-100, deposited on a substrate of 420 nm negatively charged PS particles which were arranged in f.c.c. pattern
with (111) orientation. The dip-coating lasted for 60 seconds
3.5
Theoretical Calculations
Most studies on the heterocoagulation of charged colloidal particles rely on determining the stability factor through turbidity studies [161]-[164]. However, here the
interparticle energy for colloidal particles with and without Triton-X 100 is calculated
and it is shown that the increased stability imparted by adsorbing Triton-X 100 onto
oppositely charged particles maybe the reason for ordering.
The interaction energy of geometric configurations relevant to the observed structures was calculated as follows. Following Maskaly et al., the method of Derjaguin,
Landau, Verwey and Overbeek (DLVO theory) is adapted to model interactions between oppositely charged colloidal particles. The two important interaction terms
in DLVO theory for the present systems are the vdW and electrostatic. Although
the Hogg Healy and Fuerstenau model (HHF) [165] is usually used to describe the
electrostatic behavior for heterocoagulation studies, it is valid at high ionic concentrations. Because here experiments were done at low ionic concentration, the Yukawa
pair-potential provides a good approximation to the electrostatic interaction between
......
. ...
.....
- -
-
_
'
I
two charged spheres. However, a two-particle potential may not suffice in cases where
local order produces multiple particle proximity effects. Thus, a numerical solution of
the Poisson-Boltzmann equation [166] is used to calculate the interaction interaction
energy for a collection of charged spheres.
The steric interaction between colloidal particles was modeled by using Vincents
formulation [167]. QCM measurements, described earlier in section 3.2.2 show that
the adsorption plateau is reached at close to cmc of Triton-X 100. These results are
tabulated in table 3.2. As the concentration of Triton X 100 used for the current experiments were always greater than cmc, a uniform profile for the adsorbed non-ionic
surfactant is assumed. Vincents analysis had two steric contributions for approaching
polymer or surfactant coated spheres: if 6 denotes the average thickness of the surfactant coils covering the particle surface then the interaction has an osmotic component
at intermediate separations H, i.e. (6 < H < 26) (eq. 3.2).
Table 3.2: Variation of Triton-X 100 coverage on Polystyrene with bulk concentration
of Triton- X 100, as determined by QCM
Triton-X 100 concentration in DI water
[x
cmc]
Coverage [pM/m 2
(cmc = 0.24 mM)
1.16
2.2
3.57
3.40
3.44
0.01
0.1
1.0
5.0
10.0
Eosm(6 < H < 26) = 81rkBTRlR
2
#2(0.5
- X) (
-
0.5H) 2
v1(R1 + R2)
(3.2)
At smaller separations an elastic component arises and the interaction is modeled as
shown below in eq. 3.3
Eosm(0 < H < J) = 87rkBg2
1j2#2
(0.5 - X)
(k( - 0.25n(H))
2
v1(R1 + R 2 )
where R 1 and R2 are the radii for spheres 1 and 2 respectively,
(3.3)
(3.3
# is the effective volume
....
..
...............
.............
..
.. .......
. ....
..
...
..
..............................
....
.............
fraction of the segments in the adsorbed layer, vi is the molecular volume of the solvent
29 3
and x is the Flory-Huggins solvency parameter. v1(water) = 2.99 x 10- m and X
is 0.45 for Triton-water. Using the electrostatic interaction, the interaction energy is
calculated in the absence of a surfactant, at sequential positions (fig. 3-19) of a 100
nm positive PS sphere on the surface of one of the seven negative 420 nm PS spheres
that form a close-packed layer. As shown, the most stable configuration occurs when
the positively charged particle settles into the interstice of the fixed negatively charge
particles. Although it is energetically favorable, this configuration is rarely observed
on large length-scales after spin-coating in the absence of Triton-X.
[Ix 1031
[x107
2.38
4.71
4.661
2-%
2.34
4.61M
2.31
4.57
3
2
1
4
5
6
No PS parile on a 42 nm negive PS
pelive
Posllon efta
pafrdle fom 00 subsrat [Each inuIgPr enoes a p080aIn].
Figure 3-19: Normalized electrostatic force (relative to the Brownian force) and electrostatic energy (relative to kBT ) with respect to the position of a 100 nm positive
PS sphere moving on the surface of one of the 420 nm negative PS spheres, which
are packed into close packed with fec (111) orientation. Salt concentration has been
assumed to be 0.001 mM whereas the surface charge density for each kind of sphere
has been assumed to be identical to the value supplied by the manufacturer. The calculation was done by solving the linearized Poisson Boltzmann equation for a system
of 7 negative PS spheres and one positive PS sphere through the PoissonBoltzmann
solver. For position 1, the positive PS sphere sits in the crevice formed by 3 negative
PS spheres.
02 =
45*,03
= 55*,
04=
65*,0 5= 750 and 06 = 90*
...............
PPPW-
.......
...
........
. ......
...............................
..
.....
. .........
Because thermal effects should be insufficient to produce disorder, it can be inferred that the presence of surfactant's steric hindrance promotes ordering via surface
slip after and during deposition. This surface slip is accommodated by the larger equilibrium separation. This is illustrated by fig. 3-21 where the interaction is the sum
total of the vdW, electrostatic and the steric energies. With no steric hindrance the attractive interaction produces different minimizing configurations. These observations
suggest that steric hindrance makes the primary minima (of the DLVO potential)
inaccessible and leaves the observed interstitial positions as the only energetically
favored location.
-150
DLVO+Steric at 4.a0.15
DLVO
.200
P
S-250
~1
c -300
S.350
-4000
4
3
2
1
Distance between 420 nm -ve PS and 100 nm +v* PS [nm]
5
Figure 3-20: DLVO (van der Waals + electrostatic) interaction energy (in red) and
DLVO + steric interaction energy (in blue). The above calculations are for a negative
420 nm PS and a positive 100 nm PS approaching each other in water. For the steric
interaction,
#
= 0.10, vi = 0.03nm 3 and X = 0.45
The steric interaction between colloidal particles has been widely researched and
extensive literature exists detailing the various aspects that control it ([31] and the
references contained therein). From eq. 3.2 and eq. 3.3 one of the most important
parameters in controlling the interaction is #. By changing the volume fraction of the
adsorbed surfactant one can vary the magnitude of the steric repulsion even in the
presence of very strong electrostatic attraction as modeled in fig. 3-21.
.
..............
..
... .. ...............
200
..
..
..........
.....
..........
..
.......
---....
..................
... ....
..
+=0.05
+=0.15
*=0.20
0
.200-
400
0
3
2
1
Distance between 420 nm -ve PS and 100 nm +ve PS [nns]
4
Figure 3-21: DLVO + steric interaction as a function of the adsorbed surfactant
volume fraction #
3.6
Colloidal Self-assembly on Charged Substrates:
Role of Hydrophobicity
In this section, a discussion of colloidal self-assembly on charged surfaces is presented.
In this study [156], self-assembly of negatively charged PS particles in a sessile drop,
on charged substrates, was monitored in-situ. In a sessile drop, self-assembly starts
from the edge of the drop and proceeds inwards.
In the absence of any surfactant in the system, if the particles and substrate
are oppositely charged, the assembly of colloidal particles always results in a disordered arrangement. For instance, if the assembly takes place on negatively charged
glass substrates, negatively charged PS spheres show long-range order on assembly,
whereas positively charged PS particles do not. Assembly on positively charged glass
substrates shows similar behavior. This behavior can be attributed to electrostatic
attraction between particles and the oppositely charged substrate.
The behavior of particles is more complex when a surfactant is present in the
system. Section 3.5 demonstrated that the presence of a non-ionic and amphiphilic
surfactant in a system, ensures ordered assembly of charged hydrophobic particles on
a layer of oppositely charged hydrophobic particles. As shown earlier, steric hindrance
prevents trapping of particles by attractive electrostatic potential. Consider a system
where the substrate is hydrophilic, but the particles are hydrophobic. If the surfactant
is amphiphilic and non-ionic, particle and substrate surface charges are unaffected.
Surfactants adsorb onto hydrophobic particles but not on the hydrophilic substrate.
Thus, there is no steric barrier between the particles and substrate. As a result, akin to
ordering in a surfactant-free system, charged particles form a disordered arrangement
on an oppositely charged substrate.
An interesting scenario occurs when the substrate and particles are similarly
charged, and an oppositely charged surfactant is added to the system. The behavior
of the particles depends on the hydrophobicity of the surfactant. For instance, in
one experiment, self-assembly of negatively charged PS particles was monitored on
a negatively charged substrate when (a) DTAB was present in the system and when
(b) P2VP+I- - PEO was present in the system. DTAB is a hydrophobic surfactant,
whereas P2VP+I- - PEO is an amphiphilic cationic polyelectrolyte. The mobility of PS particles in (a) was sluggish compared to the mobility of particles in (b).
Additionally, domains in (b) showed long-range order compared to domains in (a).
Since both surfactants are cationic, electrostatic interaction alone cannot describe the
above observations. It was inferred that lower mobility in (a) is caused by attractive
hydrophobic interaction between DTAB layers adsorbed on the substrate and the
spheres; due to lower mobility, the particles assembled in a disordered pattern. On
the other hand, adsorption of P2VP+I- - PEO leads to a steric barrier between
particles and the substrate. It was inferred that this led to greater mobility of PS
particles and an ordered arrangement.
3.7
Concluding Remarks
To summarize, it was shown that oppositely charged particles can be ordered in spite
of strong surface charge. A new layer-by-layer method was used to order these parti-
cles. Strong electrostatic attraction produces structures that tolerate capillary forces
during drying. The final structure is stabilized by attractive electrostatic as well as
van der Waals forces. It was found that a non-ionic amphiphilic surfactant, Triton-X
100, was necessary to produce long range ordering. Stable structures were obtained
by spin-coating positively charged particles from solution onto a fixed substrate of
negatively charged particles. By varying the concentration of particles in the suspension and the spin-speed during deposition of particles, different structures can be
obtained. A model that combines the electrostatic and vdW terms, from DLVO theory, with the steric interaction term, shows that the energetic barrier to coagulation
produced by steric hindrance along with the greater mobility afforded to the particles
by its adsorption is consistent with our observation. As a result, it is inferred that
any non-ionic amphiphilic surfactant can be used instead of Triton-X 100.
Further, it was suggested that non-close-packed zinc-blende-type structure can be
made through a layer-by-layer assembly of oppositely charged particles. Non-closepacked ordering of positively charged PS on a close packed layer of negatively charged
PS, was obtained through a dip-coating procedure.
Finally, ordering of like-charged colloidal particles on charged substrates was discussed. It was shown that hydrophobic attraction can lead to disordered aggregates
of charged particles on like-charged surfaces when hydrophobic polyelectrolytes are
used. However, use of amphiphilic polyelectrolytes can lead to the formation of ordered domains.
78
Chapter 4
Layer-by-Layer Self-Assembly of
Non-C lose- Packed
Heterostructures
4.1
Introduction
In recent years, fabrication of complete photonic band gap structures has attracted
a lot of attention. Presently, there are three methods that are widely used to make
photonic crystals. These are: colloidal assembly [106], holographic lithography [168]
and micro-machining [169]. Compared to the latter two, colloidal self-assembly is
easier, cheaper and scalable [170, 171].
However, when spherical particles spontaneously assemble, the packing fraction
and orientation of the crystal is limited to 0.74 and f.c.c. (111), respectively. At
this packing fraction, a CPBG is not observed. Photonic band gap calculations have
shown that a packing fraction of around 0.20 and a refractive index contrast of 2.5 is
required to observe a CPBG. This limitation prompted researchers to look for newer
strategies for making low-packing-fraction structures.
These strategies focused on using templates to direct the growth of colloidal crystals. The earliest templated colloidal crystals were fabricated by van Blaaderen et al.
[105]. By sedimenting silica particles from an aqueous dispersion (a process named
"colloidal epitaxy"), they were able to grow a f.c.c. colloidal crystal with (100) orientation. Colloidal epitaxy can be used to grow crystals with other orientations too.
However, it takes weeks to form a crystal through colloidal epitaxy, and the thickness
of the crystal cannot be controlled. In comparison, vertical deposition methods (such
as convective assembly), are best suited for use with templates, as they offer control
over thickness during colloidal assembly.
Recently, Santamaria et al. [14] proposed a novel approach for making a CPBG
diamond cubic crystal. They fabricated a b.c.c. crystal, composed of interpenetrating
diamond cubic, silica and polymer lattices. In the end of the process, they removed
the polymer particles and obtained a diamond cubic structure made of silica particles.
Their approach was based on two facts. These were (i) a body centered cubic (b.c.c.)
lattice is made of two interpenetrating diamond cubic lattices and (ii) a b.c.c. lattice
is easier to grow since sphere sites are stable in it. Santamaria et al. used the following
procedure: a silicon template with holes patterned in (110) symmetry was used to
direct the assembly. By using a robot attached to a SEM, polystyrene (PS) particles
were placed in alternate holes and silica particles in the remaining holes. This process
was repeated particle by particle and layer by layer to make a b.c.c. crystal. In the
end, PS particles were removed by etching in oxygen plasma. The silica particles that
were left behind, were arranged in a diamond cubic structure. In principle, robotic
assembly can be used to form any non-close-packed structure, so long as particles are
in contact with one another. However, it is evident that there is a need for a more
efficient and less expensive method to make non-close-packed structures.
In this chapter, templated self-assembly of an ordered 2D heterostructure of likecharged PS and silica particles is described [24, 172].
A silicon wafer with holes
patterned in (100) symmetry is used as a template. Particles are arranged in the
heterostructure akin to the pattern on a checkerboard; PS particles reside in every
other hole and silica particles fill the remaining holes. A two-step convective assembly
process is used to form this structure. In the first step, it is shown that PS particles
form a sparse structure if the Debye length (r-1) of the solvent and concentration of
particles is correctly controlled. Domains with a sparse arrangement of PS particles
are hundreds of micrometers large; these domains are referred to as Li-PS. In the
second step, convective deposition is used to fill the remaining holes with silica particles. The resulting 2D heterostructure domains in the first layer (hereafter, referred
to as Li) are tens of micrometers large.
Compared to earlier methods, this technique relies on self-assembly of charged
particles to produce a sparse domain and a 2D heterostructure. By replicating the
process above, layer by layer, one can create a multilayered heterostructure with two
particle types. Removal of one particle type from the final heterostructure leads to
a non-close-packed multilayered structure. For example, it is shown that a two-layer
heterostructure of silica and PS is formed by layer-by-layer assembly. In the end of the
process, PS particles are removed. This leaves behind a two-layer non-close-packed
structure of silica particles.
4.2
4.2.1
Materials and Methods
Materials
Suspensions of monodisperse polystyrene (PS) beads measuring 250 nm (sulphate
functionalized, (= -52.56 mV at ,-'= 127 nm, and charge density measured by the
manufacturer equal to -0.019 C/m 2 ), 140 nm (sulphate functionalized, (= -54.62 mV
at r-'= 127 nm, and charge density measured by the manufacturer equal to -0.011
C/m 2 ) and 500 nm (sulphate functionalized, (= -61.57 mV at K-= 127 nm, and
charge density measured by the manufacturer equal to -0.041 C/rm2 ) were purchased
from Molecular Probes Inc., Eugene, OR. Suspension of monodisperse carboxyl functionalized PS particles was also bought from the same supplier (it had (= -52.56
mV at ,-=
127 nm, and charge density measured by the manufacturer equal to -
0.032 C/m 2 ). Monodisperse silica suspension of 250 nm particles was purchased from
Corpuscular Incorporated. It had (= -45.54 mV at K-'= 127 nm. Electrophoretic
mobility for different colloidal samples was measured using a Zeta-PALS (Brookhaven
Instruments Corporation). Once electrophoretic mobility was measured, zeta potential was calculated using the Smoluchowski model (eq. 2.34). All the above suspensions were dialyzed against de-ionized (DI) water to lower their salt concentrations
before use.
Poly(allylamine hydrochloride) (PAH; M.=50,000) was purchased from Sigma
Aldrich Inc. Polyelectrolyte solutions were prepared by thoroughly mixing appropriate amounts (1 mg/ml to 7 mg/ml) of powdered PAH in DI water.
4.2.2
Solvents
De-ionized water (DI water) was used for most of the experiments and was readily
available. However, in a few cases, 99% anhydrous Ethyl Alcohol (Hubbard Hall
Inc.) was used as a solvent. Ethanol-based silica suspensions were prepared via the
following procedure: silica particles were centrifuged from 10 ml of their original
aqueous suspension.
Then they were transferred to 10 ml ethanol. The ethanol
suspension was sonicated for 60 minutes. Thereafter, the particles were centrifuged
again and resuspended in ethanol. Centrifuging and resuspension of the particles was
repeated five times.
Conductivity of DI water was measured (YSI 3200 Conductivity Instrument) in
the absence of particles, and these values were used to infer the Debye lengths. Large
Debye lengths were obtained for the particle suspensions as a result of: i) dialysis of
the particle suspensions (dialysis was used to lower salt concentrations in the particle suspensions). Particles were dialyzed against DI water in Float-a-lyzer dialysis
bags from Spectrum Labs. These bags allow salt ions to diffuse into DI water while
preventing the diffusion of particles at the same time. The salt concentration of the
particle suspension was tracked by measuring the conductivity of the reference solvent, and the process continued until no further change in the conductivity of the
reference solvent could be detected; and ii) low concentration of particles. Since low
particle concentration was used for the experiments, the concentration of particle
counter-ions was also low. Calculations showed that although the particle counterions led to a drop in Debye length, the Debye length in the suspension was large
enough to influence long-range interparticle interaction.
4.2.3
Template Preparation
Silicon templates with pitches = 185 nm, 330 nm or 660 nm, were prepared by
interference lithography (IL). The procedure for this is outlined in section 3.2.4. These
templates had holes arranged in a pattern with (100) symmetry. Fig. 4-1 is a SEM
image for a template with a pitch of approximately 330 nm.
Figure 4-1: SEM image of a silicon template, which has holes arranged in a pattern with (100) symmetry. The holes were 45 nm deep. This template was created
according to the procedure described in section 3.2.4
All templates had holes with a depth of 45 nm. For optimum results, the following
two factors were controlled:
Diameter of the hole
Diameter of the particle
A2
=
Pitch of the template
Diameter of the particle'
(4.1)
(4.2)
4.2.4
Colloidal Assembly
Prior to all particle deposition steps, templates were treated with oxygen plasma at
6 mTorr for 10 seconds. Subsequent contact angle measurements showed the wetting
angle of water to be between 0* and 60. Fig. 4-2 is an image with a drop of water
on a bare template. A droplet of water was placed on a bare template and it spread
immediately. In fig. 4-2 the droplet is visible. Here, the contact angle was 0.800.
Particles were assembled through convective assembly. In this process, templates
Siio
Te
plt
Figure 4-2: Contact angle measurement on a bare silicon template after exposure to
oxygen plasma. The contact angle was 0.80'.
were attached to the side-walls of a beaker, with the particle suspension. When
the suspension was slowly withdrawn, particles assembled on the template. For PS
particle assembly, a 8-v/v% suspension was diluted in DI water (Debye length = 204
nm) to 0.025-v/v%. Thereafter, a beaker with PS suspension and templates, was
placed in a water bath at 35'C. Silica particles were assembled as follows. A 5-v/v%
aqueous suspension of silica was diluted to 0.025-v/v%. Thereafter, a beaker with
this suspension and substrates, was placed in a water bath at 50'C.
Unless otherwise stated, the withdrawal speed of the suspension during all deposition steps was 46.1 pm/min.
4.3
4.3.1
.....
.....
........
......
.............
-------------
.....................
.........
...........
............
............
.
Results
Li-PS: Sparse Polystyrene Layer
When PS particles are assembled on a template, the final arrangement depends on
the concentration of PS particles in the dispersion and the Debye length of the solvent. Fig. 4-3 is a schematic and shows the different kinds of ordering seen on the
template during this work. Convective assembly of PS particles is characterized by
Close-packed
Ordering
IAll
ISparse
holes on the
template occupied
Ordering
Figure 4-3: Schematic showing the different kinds of ordering seen on the template.
the formation of bands (consisting of sparse domains) separated by regions without
any particles. This is shown in fig. 4-4 and is attributed to the stick and slip of
meniscus on the template [173]. The effect of stick and slip is characterized through
Aband
(eq. 4.3) and 6 band (eq. 4.5), whereas the extent of sparse ordering, within a
band, is characterized through
qOsparse
(eq. 4.4):
,\band = Average center-to-center distance between two bands.
qOsparse =
Average area of a band, which is occupied by the sparse pattern.
(4.3)
(4.4)
(4.5)
Jband = Average width of a band.
Fig. 4-5, fig. 4-6 and fig. 4-7 show scanning electron microscope (SEM) images
of the final arrangement of PS particles on the template when the Debye length was
fixed at 204 nm and the concentration of particles was 0.01-v/v%
,
0.025-v/v% and
Figure 4-4: SEM image of a template after convective assembly of PS particles from
a 0.025-v/v% aqueous suspension. Due to stick and slip of the meniscus, the particles
assemble in bands, separated by regions on the template without any particles. In
this image, bright regions are bands of PS particles, whereas dark regions are regions
on the template without any particles
0.10-v/v%, respectively. Insets in these figures schematically show the arrangement
of PS particles on the template. In these insets, PS particles on holes are shown in
red and the empty holes are shown as open circles. The pair distribution function
(PDF) for the arrangement of PS particles in the SEM images above, are plotted
in fig. 4-8 and fig. 4-9 respectively. Fig. 4-10 is a SEM image, showing the side
view of a template with Li-PS arrangement. Fig. 4-11 is a SEM image showing
the arrangement of PS particles when the Debye length was 30 nm; concentration of
particles for this experiment was 0.025-v/v%. The PDF for the arrangement of PS
particles in fig. 4-11 is plotted in fig. 4-12.
Aband,
#sparse, and
6
band
for the above
experiments are summarized in table 4.1:
When 0.1-v/v% suspension was used, an increase in polydispersity led to the formation of close-packed domains. In contrast, at lower concentrations (0.01-v/v% and
0.025-v/v%) the assembled pattern withstood larger fluctuations in dispersity and retained the sparse pattern. However, even at these concentrations, a few domains with
close-packed order, and with PS particles occupying all holes on the template, were
.........
..............
I......
.......
Table 4.1: Variation in Aband, #,parse, and
centrations for 250 nm PS particles
K-1
204nm
204nm
30nm
concentration
0.025-v/v%
0.01-v/v%
0.025-v/v%
6
band
at different Debye lengths and con-
Aind [um]
#sparse
27.6±13.24
40.1+20.12
25.1±12.39
0.90±0.10
0.91±0.06
0.19±0.09
5
band
[PM]
15.2±7.5
8.0±3.4
14.9±7.6
Figure 4-5: SEM image of a template, after convective assembly of 250 nm PS particles from a 0.01-v/v% aqueous suspension. The withdrawal speed of the suspension
was 46.1 pm/min at 35*C. i-' was 204 nm. This was inferred from conductivity measurement of the solvent. As seen in this image, particles arrange in a sparse pattern.
The inset shows a schematic arrangement of particles on the template: red circles
denote particles and open circles denote empty holes. Due to the low concentration
of the particles in suspension, narrow bands of PS particles assemble on the template.
..
...
....
.......
....
.
Figure 4-6: SEM image of a template, after convective assembly of 250 nm PS particles
from a 0.025-v/v% aqueous suspension. The withdrawal speed of the suspension
was 46.1 pm/min at 35'C. r-1 was 204 nm. This was inferred from conductivity
measurement of the solvent. As seen in this image, particles arrange in a sparse
pattern. The inset shows a schematic arrangement of particles on the template: red
circles denote particles on holes and open circles denote empty holes.
.......
......................wa
---
.. ----
-
.
-
Figure 4-7: SEM image of a template after convective assembly of 250 nm PS particles
from a 0.1-v/v% aqueous suspension. The withdrawal speed of the suspension was
46.1 pm/min at 35'C. r- was 204 nm. This was inferred from conductivity measurement of the solvent. Due to high concentration of PS particles in the suspension,
they fill all the holes in the template. The inset shows a schematic arrangement of
particles on the template. Red circles denote PS particles on holes.
I
2
..
.*I..
.3I.
4
I
6
d
8a
.
.
.
I
10
.
.
.
I
12
.
.
.
I
14
Figure 4-8: Plot of the pair distribution function for the arrangement of 250 nm PS
particles in fig. 4-5 and fig. 4-6. o is the diameter of the sphere
.........
3 -
2-
3....
.I....I..I.
1
2
4
6
8
10
12
14
16
Figure 4-9: Plot of the pair distribution function for the arrangement of 250 nm PS
particles in fig. 4-7. o-is the diameter of the sphere
Figure 4-10: SEM image of the cross-section of a template with 250 nm PS particles
ordered in Li-PS arrangement
..........
..
"I'll"
Figure 4-11: SEM image after convective assembly of 250 nm PS particles from a
0.025-v/v% aqueous suspension. The withdrawal speed of the suspension was 46.1
pm/min at 35 C. r, 1 was 30 nm. This was inferred from conductivity measurement
of the solvent. Random filling may be associated with the reduced Debye length.
I
i
.
,
i
2
.
.
.
i
4
.
.
.
i
6
.
.
.
.
861
.
.
-
-
I
.
10
12
14
16
Figure 4-12: Plot of the pair distribution function for the arrangement of 250 nm PS
particles in fig. 4-11. a is the diameter of the sphere. Due to low r-', the arrangement
shows short-range order compared to the arrangement of particles in fig. 4-6
observed. In general, the number of close-packed domains and their size, decreased
on lowering the concentration of particles. Due to stick and slip of the meniscus, the
domains with sparse order were bigger, perpendicular to the direction of withdrawal
of the suspension. Thus, typical Li-PS domains were 15prm wide along the pumping
direction, and hundreds of micrometers large, perpendicular to the direction of withdrawal of the suspension. A SEM image of a typical Li-PS domain is shown in fig.
4-13.
Figure 4-13: SEM image of a large area of the template after convective assembly
of 250 nm PS particles from their 0.025-v/v% aqueous suspension. The withdrawal
speed of the suspension was 46.1 pum/min at 35'C. r- was 204 nm. This was inferred
from conductivity measurement of solvent. This image shows a Li-PS band where
PS particles are arranged akin to their arrangement in fig. 4-6. Thus, typical Li-PS
domains were 15 pam wide along the direction of withdrawal of the suspension and
hundreds of pm large, perpendicular to it.
4.3.2
Results and Discussion:
Mechanism of Sparse Struc-
ture Formation
Orientation of the template during convective assembly plays a key role in the formation of the sparse structure. In a set of experiments, the template was fixed such
that the holes are oriented along (100), (110) and (120), relative to the direction of
...............
....
.......
......
withdrawal of the suspension. Results from these experiments are shown in fig. 4-14
and fig. 4-15.
Fig. 4-14 is a plot
50
----
Of
oband and Aband,
and fig. 4-15 is a plot Of #sparse for
Yband
band
30
10
(100)
(110)
Orientation of the template
(120)
Figure 4-14: Variation of Aband and Jband when PS particles were assembled onto
templates, fixed at different orientations relative to the direction of withdrawal of the
suspension. The suspension was withdrawn at 46.1pm/min at 35'C.
different orientations. Fig. 4-15 shows that
,,,arse is larger if the template is oriented
along high-symmetry directions ((110) and (100)), with respect to the direction of
withdrawal of the suspension. When the template is oriented along a high-symmetry
direction, such as (100), holes on the template are oriented parallel to the meniscus.
On the other hand, when the template is oriented along a low-symmetry direction,
such as (120), the holes are not oriented parallel to the meniscus. This may indicate
that PS particles are stabilized in a non-close-packed pattern at the three-phase line
(i.e. the meniscus), prior to their deposition on the template. It is shown later that
this is due to electrostatic repulsion between particles.
4.3.3
Discussion: Conditions for Sparse Structure Formation
Dependence of the final arrangement of particles can be interpreted with the following
ratio, A3 . This is given by eq. 4.6.
0.8
0.4-9
0.0 ,j
(100)
(120)
(110)
Orientation of the template
Figure 4-15: Variation of #sparse when PS particles were assembled onto templates,
fixed at different orientations relative to the direction of withdrawal of the suspension.
The suspension was withdrawn at 46.1prm/min at 35'C.
Diameter of the particle
Debye length of the solvent
(4.6)
It was verified that formation of sparse PS domains is not restricted to 250 nm
sized particles. In fact, sparse domains were observed when 140 nm and 500 nm PS
particles were assembled on their respective templates at 35 C. The Debye length
was 204 nm and the concentration of PS particles in the dispersion was 0.025-v/v%
for both experiments. When
-1 = 204 nm, A3 is 0.408 in a dispersion of 500 nm
particles, whereas it is 0.816 for 250 nm particles and 1.46 for 140 nm particles.
Detailed Monte Carlo simulations, discussed in chapter 6, show that the concentration of particles and K- play a central role in the formation of domains with sparse
arrangement of particles. Besides these two, the other parameters that were controlled
for obtaining large domains with sparse ordering are briefly discussed below.
Hydrophobicity
Surface treatment of starting templates played a key role during convective deposition.
When the surface of the template was hydrophobic, the meniscus at the air-water interface had a higher concentration of particles. As a result, multiple layers assembled
during deposition. On the other hand, when the surface was super-hydrophilic (wetting angle for water ~ 00), a monolayer of particles assembled. Common methods
to make the template super-hydrophilic are, treatment with Pirhana (3:1 mixture of
sulphuric acid and hydrogen peroxide respectively) or exposure to oxygen plasma.
Plasma treatment was used instead of the Pirhana treatment because of its effectiveness and handling.
Withdrawal Rate of the Suspension
The largest bands of sparsely ordered PS particles were obtained when withdrawal
speed was 46.1 pm/min. At faster speeds, narrower bands with sparse order were
observed, whereas at a slower speed (23.3 pim/min) wider bands with low
#sparse
were observed. The most likely explanation for this is the variation in concentration
at different withdrawal speeds. When the withdrawal speed is slow, more particles
migrate to the air-water interface. As a result, dense packing of particles is more
likely. On the other hand, at high withdrawal speeds, a monolayer is formed because
fewer particles migrate to the air-water interface. These results are summarized in
table 4.2.
Table 4.2: Formation of the sparse structure at different speeds of withdrawal of the
suspension
Speed of withdrawal
of the suspension[pm/min]
46.1
23.3
Aband
[/-Lm]
27.6+13.24
12.67+6.33
#sparse
0.90+0.10
0.60+0.09
oband
[pm]
15.2±7.5
21.2+5.2
.
.
' -. '- '---'..................
..........
...........
...........
....
4.3.4
---
--
-
T
- II --
_-
-
-
Li-Silica
Li-PS was used as the starting substrate for deposition of silica particles. Before
deposition, Li-PS was exposed to oxygen plasma for 10 seconds.
Contact angle
measurements showed that the surface is hydrophilic, with a wetting angle between 0*
and 60. As previously discussed, a super-hydrophilic surface is required for assembling
a monolayer through convective assembly. Fig. 4-16 is an image of a drop of water on
a Li-PS substrate, after exposure to oxygen plasma. The droplet spread immediately
on coming in contact with the substrate. However, it is visible in fig. 4-16. The
contact angle for this experiment was 4.7*.
Figure 4-16: Contact angle measurement on Li-PS substrate, after it was exposed to
oxygen plasma for 10 seconds. The contact angle of water was 4.7*
Silica particles were deposited from a 0.025-v/v% suspension at 46.1 pm/min and
50'C. The arrangement of these particles is also characterized by the formation of
bands. Thus, bands with silica particles, arranged in a sparse pattern (hereafter,
referred to as Li-silica) were separated by regions without silica particles.
When the assembly was carried out at 35*C, silica particles occupied fewer holes
on the substrate. This could have been due to the higher sedimentation of silica
particles. Various methods have been used to reduce sedimentation. Most researchers
-
use silica dispersion in ethanol instead of DI water [127]. Since ethanol is more volatile
than water, a greater number of silica particles are transported to the meniscus.
Other researchers prefer to assemble silica particles on a horizontal template, using
gravitational force to their advantage [2]. In the present set-up, ethanol is not an
appropriate dispersion medium because PS particles are partially soluble in ethanol
and become inflated. For instance, fig. 4-17 is a SEM image and shows inflated PS
particles (~ 350 nm) that were originally 250 nm in diameter. These were exposed
to ethanol during deposition of silica particles from a silica dispersion in ethanol.
Assembly on a horizontal template is also not preferable because the thickness of
the final structure cannot be controlled, unlike in vertical deposition. The preferred
approach is to assemble particles from their aqueous dispersion at 50*C. During this
process, the beaker was partially immersed in a water bath at 50'C. This created
convective currents that transported more particles to the meniscus and reduced the
effect of sedimentation.
Figure 4-17: SEM image of a template with 250 nm PS particles arranged on the
template. This image was taken after silica particles were assembled from a 0.025v/v% ethanol suspension, on a substrate with 250 nm PS particles arranged on the
template. PS particles are partially soluble in ethanol. As a result, they swell to 350
nm and coalesce
Fig. 4-18 is a SEM image showing bright silica particles and dull PS particles,
ordered in the first layer. The contrast was a result of different material composition
of these particles. Fig. 4-19 is a SEM image showing a larger area of the first
layer. Note that bands of silica particles only partially overlap with bands of PS
particles. As a result, Li domains were smaller than Li-PS domains. Typically,
Asilica-bands
was 26.1 pum, #5 L was 0.70 and
silica-bands
was 8.74 pm.
This is the
Figure 4-18: SEM image showing the arrangement of 250 nm silica and PS particles,
after silica particles were assembled from a 0.025-v/v% aqueous suspension, at 50*C,
on Li-PS substrate. The speed of withdrawal of the suspension was 46.1 pm/min.
This kind of order is referred to as L1. PS particles appear dark and silica particles
appear bright. The contrast is due to different material composition
first experimental demonstration of self-assembly being used to form a 2D non-closepacked heterostructure. The structure was formed on a template and stabilized by
repulsive electrostatic interaction between particles. Ionic colloidal crystals (ICCs)
are non-close-packed structures too. However, they collapse into a close-packed or
disordered structure on removal of the solvent.
By controlling the repulsive electrostatic potential between particles, multiple
structures can be nucleated on a template. For instance, fig. 4-20 shows a SEM
image, where PS particles formed a sparser structure. This structure were stabilized
when concentration of PS particles was 0.01-v/v% and A3 ~.0 *. The empty sites
*In this structure, second nearest neighbors are seperated by 737.9 nm. Even at this distance, and
Figure 4-19: SEM image of a large area with Li ordering. This region is made of dark
250 nm PS particles arranged in every other hole and bright 250 nm silica particles
filling the remaining holes. The contrast is due to different material composition.
Typical bands with Li order were 8 pm wide along the direction of withdrawal of the
suspension, and tens of micrometers large, perpendicular to it
were filled in the second step with silica particles. Fig. 4-21 is a SEM image taken
after silica particles were deposited in the second step.
Figure 4-20: SEM image of a template after convective assembly of 250 nm PS particles from their 0.01-v/v% aqueous suspension. The withdrawal speed of the suspension was 46.1 pm/min at 35'C and r- was 250 nm. This was inferred from
conductivity measurement of the solvent. Due to low concentration of PS particles
in the suspension and due to high r,, sparser pattern was stabilized by electrostatic
repulsion between particles
Formation of sparse structures is not restricted to the present template. Templates with other geometries can be used to nucleate different 2D heterostructures.
Fabrication of a stable 2D heterostructure is the key to 3D assembly of non-closepacked colloidal architectures. In the present study, a two-layer non-close-packed
heterostructure was made by layer-by-layer assembly of the 2D heterostructure described in section 4.3.3. Similar to the formation of L1, the formation of the heterostructure in the second layer (L2) was a two-step process. In the first step, PS
particles formed a sparse pattern on L1. This pattern is referred to as L2-PS. In the
next step, unoccupied sites in L2-PS were filled with silica particles.
K-1= 250 nm, electrostatic interaction energy is approximately 2370kBT and may be responsible
for stabilizing this structure.
100
Figure 4-21: SEM image of 250 nm bright silica particles and 250 nm dark PS particles
arranged on a template. Silica particles were deposited on a template with PS particles arranged in a sparser pattern, shown in fig. 4-20. Silica particles were deposited
from a 0.025-v/v% aqueous suspension at 500 C. The suspension was withdrawn at
46.1 pm/min
4.3.5
L2-PS
In the second layer, sparse domains of PS particles were smaller than sparse domains
in the first layer. As before, deposition of PS particles was preceded by a 10-second
exposure to oxygen plasma. A 0.025-v/v% aqueous suspension of PS particles was
used for deposition; Debye length in the suspension was 204 nm. Due to stick and
slip of the meniscus, the deposition was characterized by the formation of bands of
PS particles, separated by regions without particles. Typically, these bands were 5
pm wide. Fig. 4-22 is a SEM image of a band of PS particles in the second layer.
Fig. 4-23 is a SEM image showing a smaller region with L2-PS ordering. For clarity,
PS particles in L2-PS (in fig. 4-23) are colored in bright green. The colored image is
shown in fig. 4-24. Dull green circles represent vacant L2-PS sites.
When the PS suspension was withdrawn at 46.1 pm/min, L2-PS domains were
only a few particles large. Larger L2-PS domains were observed when the suspension
was withdrawn at 23.3 pm/min. Further reduction in the withdrawal rate led to the
101
Figure 4-22: SEM image of a large area with 250 nm PS particles arranged in a sparse
pattern in the second layer. The underlying first layer had Li order. PS particles
were deposited from a 0.025-v/v% aqueous suspension at 23.3 pm/min and 35'C,
through convective assembly. Typical bands with L2-PS order were 5 pm wide.
102
..
. .......
Figure 4-23: SEM image of a region with 250 nm PS particles arranged in a sparse
pattern on the second layer. The underlying, first layer had Li order. PS particles
were deposited from a 0.025-v/v% aqueous suspension at 23.3 [pm/min and 35*C,
through convective assembly
GRAIN I
GRAIN 2
GRAIN 3
Figure 4-24: PS particles in L2-PS in fig. 4-23, are colored in green. Dull green
discs denote vacancies, whereas bright green discs denote PS particles. Here, L2-PS
domain is made of three L2-PS grains. These are represented by coloring the rim of
the discs differently. Discs with identically colored rims belong to the same grain
103
. ........
. ..
. . ......................
formation of close-packed bands without affecting the size of sparsely packed L2-PS
domains. Interestingly, larger regions of sparse L2-PS domains were observed when
the underlying layer was made solely of PS particles. Fig. 4-25 is a SEM image
showing sparsely ordered PS particles arranged on a first layer of PS particles.
Figure 4-25: SEM image of a region with 250 nm PS particles arranged in a sparse
pattern in the second layer. In the first layer PS particles occupy all the holes. Larger
domains of PS particles with sparse ordering were observed when the underlying layer
was made solely of PS particles. Here, PS particles were deposited in the second layer
0
from a 0.025-v/v% aqueous suspension at 23.3 pm/min and 35 C, through convective
assembly
4.3.6
L2-Silica
After deposition of PS, the substrate was exposed to oxygen plasma for 10 seconds.
Thereafter, silica particles were deposited through convective assembly. Due to stick
and slip, the deposition was characterized by the formation of bands along the direction of withdrawal. However, there was negligible overlap between L2-PS and bands
with sparsely ordered silica particles (hereafter, referred to as L2-silica). It was found
that a reduction in the electrostatic repulsion between particles plays a key role in
increasing the overlap of L2-silica with L2-PS. In addition, relative humidity (RH)
104
was also varied but had negligible effect on the overlap between L2-PS and L2-silica
bands. Details of these experiments are discussed below.
Electrostatic Interaction
During deposition of silica, the suspension was maintained at 50'C and withdrawal
speed was 46.1pm/min. The interaction potential between the substrate and silica
particles in the suspension was repulsive, as all the particles were negatively charged.
It was modified as follows:
(i) Ionicity in the suspension: Ionicity was modified by changing the concentration
of sodium chloride (NaCl) in the suspension. However, even at moderate (1.6 x 10-5
M) and high (10- M) ionicity, overlap of L2-silica and L2-PS bands was negligible.
(ii) Charge on the substrate: The charge on the substrate was modified by dipcoating the substrate with a cationic polyelectrolyte. Researchers have often used
layer-by-layer assembly of polyelectrolyte on a layer of assembled colloids [174], to reduce or reverse the surface charge. In the current study, Poly(allylamine hydrochloride) (PAH) was used to reduce the surface charge. Although I had no means to
quantify the variation of surface charge, larger regions of overlap between L2-PS and
L2-silica bands were observed after longer exposure to PAH. Larger regions of overlap
were also observed when denser suspensions of PAH were used during dip-coating.
This may have led to greater reduction of the surface charge by adsorption of PAH.
Dipping in PAH was carried out by changing the dipping time in PAH (at constant
PAH concentration) and by changing the concentration of PAH (at constant dipping
time). Table 4.3 summarizes these values.
Table 4.3: Summary of Dip-coating in PAH
Concentration of PAH
in the suspension [mg/ml]
1
1
3
7
105
Dipping time in PAH
suspension [minutes]
5
10
5
5
.......................
..
....
......
........
.................
......
....
.
- - --____
40
-----
-
Yband
band
E
20-
3
Concentration of PAH [mg/ml]
7
Figure 4-26: Variation of Asilica-band and 6 silica-band for silica particles after dip-coating
in different suspensions of PAH
Fig 4-26 shows the variation in Asilica-band and
the variation of
4-27,
#L2
#L2
6
silica-band,
and fig. 4-27 shows
on changing the dipping conditions in PAH. According to fig.
is zero until the samples were dipped in PAH. When samples were dipped
in 1 mg/ml PAH suspension, small regions with L2 order (#L2 =0.05) were observed;
larger
6
silica-band
was also observed. Fig. 4-28 is a SEM image showing a substrate
that was dipped for 10 minutes in a 1 mg/ml suspension of PAH, followed by the
assembly of silica particles. For better visual contrast, silica and PS particles in the
second layer are colored red and green, respectively. The colored image is shown in
fig. 4-29. However, according to fig 4-26, largest regions with L2 order were observed
when samples were dipped in 3 mg/ml suspension of PAH for 5 minutes, followed by
silica deposition (#L2=0-19). Fig. 4-30 is a SEM image and shows a region of overlap,
L2, which has been circled. For better visual contrast, silica and PS particles in the
second layer are colored red and green, respectively. The colored image is shown in
fig. 4-31.
When silica particles were deposited on substrates that were dipped in 7 mg/ml
suspension of PAH for 5 minutes, many silica particles were perched on top of the
underlying PS particles.
This is shown in fig.
106
4-32. Enclosed in the box, is a
0.2
0.1
0 --
0
3
1
Concentration of PAH [mg/ml]
7
Figure 4-27: Variation of #L2 after dip-coating in different suspensions of PAH
Figure 4-28: SEM image after 250 nm silica particles were deposited in the second
layer, from a 0.025-v/v% aqueous suspension at 50*C and 46.1 pm/min, through
convective assembly. Prior to silica deposition, the substrate was dipped in 1 mg/ml
suspension of PAH for 10 minutes
107
..........
....
Figure 4-29: Identical SEM image to fig. 4-28. PS particles in the second layer are
colored green and silica particles in the second layer are colored red, for better visual
contrast. The colored particles form a L2 domain
Figure 4-30: SEM image after 250 nm silica particles were deposited in the second
layer, from a 0.025-v/v% aqueous suspension at 50*C and 46.1 pim/min, through
convective assembly. Prior to silica deposition, the substrate was dipped in 3 mg/ml
suspension of PAH for 5 minutes
108
Figure 4-31: Identical SEM image to fig. 4-30. PS particles in the second layer are
colored green and silica particles in the second layer are colored red, for better visual
contrast. The colored particles form a L2 domain
silica particle perched on a PS particle.
This kind of arrangement may indicate
that the surface charge of the substrate was reversed. According to fig. 4-26 this is
accompanied by the formation of larger bands (typically
6
sizicands,
=25.19pm and
#L2=0.11).
Relative Humidity (RH) and Hydrophobicity
Researchers have found that stick and slip of the meniscus can be reduced by using a
super-hydrophilic template [143]. Indeed, before every deposition step, the substrate
was exposed to oxygen plasma for 10 seconds. In addition, the following conditions
were used.
In one set-up, carboxyl-functionalized PS particles were used for Li-PS and L2-PS
steps, instead of sulphate-functionalized PS particles. Although both are negatively
charged, carboxyl-functionalized particles are hydrophilic. Consequently, stick and
slip of the meniscus should be further reduced during formation of PS and silica
bands. However, it was found that, irrespective of the functionality of PS particles,
ordering of PS and silica particles led to formation of similar sized bands.
109
Figure 4-32: SEM image after 250 nm silica particles were deposited in the second
layer, from a 0.025-v/v% aqueous suspension at 50'C and 46.1 pm/min, through
convective assembly. Prior to silica deposition, the substrate was dipped in 7 mg/ml
suspension of PAH for 5 minutes. Note that a negatively charged silica particle is
perched on top of another particle in the first layer. This may indicate that charge
reversal took place for particles in the first layer, after dipping in the 7 mg/ml suspension of PAH
110
........................
...
...
............
.. .....
---
....
....
...........
.. .....
.........
-__---
Table 4.4 shows that Li-PS bands formed from carboxyl and sulphate functionalized particles have similar characteristics.
Table 4.4: Characteristics of Li-PS bands from carboxyl and sulphate functionalized
PS particles
Functionalization of
PS particles
sulphate
carboxyl
Aband
[pm]
27.6+13.24
25.1+12.35
#sparse
0.90±0.10
0.85+0.07
5
band
[Am]
15.2+7.5
14.3+6.85
In another experiment, deposition of silica particles was carried out at different
relative humidities (RH). It has been shown that stick and slip of the meniscus can be
reduced at high RH [143, 175]. Fig. 4-33 is a plot of the characteristics of the bands
of silica particles after deposition. As shown here, an increase in RH leads to wider
bands; at RH= 80%, no particles are deposited on the template due to high slip on
the template. However, silica particles have close-packed order in these bands. As a
result,
#L2
was approximately 0 at all relative humidities. A plot of
4L2
is shown in
fig. 4-34.
-e
50 50
*
6
band
band.
30
E
10-
30
70
60
50
40
Relative Humidity [%]
80
Figure 4-33: Variation of Asilica-band and 6 silica-band after deposition of silica particles
at different relative humidities.
111
0.1
U.U *EI
-0.1
30
Figure 4-34: Variation of
humidities
4.3.7
#L2
70
60
50
40
Relative Humidity [%]
80
after deposition of silica particles at different relative
L2
From the above discussion, one can infer that optimum domains of L2 were obtained
when L2-PS substrates were dipped in 3 mg/ml PAH suspension for 5 minutes. L2 is a
two-layer heterostructure formed from PS and silica particles. A low volume fraction
silica structure was obtained from this heterostructure by removing the PS particles,
without disturbing the silica ones. Latex calcination was not considered for this
purpose because it produced liquid latex, which dragged the silica beads by surface
tension and caused the structure to collapse. Therefore, a more gentle method was
used: oxygen plasma etching at 6 mTorr for 7 minutes. Plasma selectively removes
PS and hardly affects the silicon wafer or silica particles.
Fig. 4-35 shows a SEM image of the resulting structure after removal of PS
spheres. Fig. 4-36 and fig. 4-37 show a close-up of the top view and the crosssection of the resulting structure.
#non--close-packed, and
Typically, average values for
Anon--close-packed
6
non--close-packed,
are 24.2pm, 0.11 and 51.2 pm respectively.
112
Figure 4-35: SEM image showing a band of 250 nm silica particles arranged in a 3D
non-close-packed structure. PS particles were removed from the sample by exposure
to oxygen plasma.
113
Figure 4-36: SEM image of 250 nm silica particles arranged in a 3D non-close-packed
structure. PS particles were removed from the original sample by exposure to oxygen
plasma
Figure 4-37: SEM image of a cross-section of a template with 250 nm silica particles
arranged in a 3D non-close-packed structure
114
4.4
Concluding Remarks
In summary, it was shown that a sparse pattern of PS particles on a template was
obtained by convective assembly. This was obtained at high Debye length in the solvent and low concentration of particles in the suspension. It was further shown that
at low Debye length or high concentration of particles, the sparse pattern cannot be
stabilized. The sparse pattern was used to make an ordered 2D heterostructure of
PS and silica particles. This was fabricated by deposition of identically sized silica
particles in the empty sites of the sparse pattern. Compared to traditional methods
of obtaining 2D heterostructures, this method is facile, faster, scalable and can potentially produce layers with different symmetries, governed by template geometry.
Additionally, a layer-by-layer method of making 3D heterostructures from 2D heterostructures was proposed. Through this method, a two-layer heterostructure of PS
and silica was fabricated. Removal of PS particles from the final assembly led to a
non-close-packed structure of silica particles. This structure represents the first two
layers of a CPBG diamond cubic unit cell. Because self-assembly is used, one is not
limited by the particle and solvent type, as long as the process conditions are correctly
controlled. Stick and slip of the meniscus was identified as the main impediment in
obtaining large domains.
115
116
Chapter 5
Stick and Slip During Convective
Assembly
In chapter 4, it was shown that convective assembly of colloids leads to the formation
of bands with particles separated by regions without any particles. This stripe pattern
is formed due to stick and slip of the meniscus on the template. A reduction in stick
and slip may lead to larger bands
( 6 band,
eqn. 4.5) and therefore larger domains with
sparse structure. Recently, a few methods have been proposed that can prevent stick
and slip [145, 176, 177]. Thus, the applicability of these methods to the present set-up
is discussed.
The vertical deposition method was developed by Nagayama et al. [122]. They
showed that the main factors that contribute to the ordering of particles are the
attractive capillary attraction between particles and the convective transport of the
suspension to the meniscus. It was further shown that stick and slip of the meniscus during horizontal deposition is a result of the competition between the surface
tension of the deposited film,
YDF,
surface tension of the suspension, 7Ys, and the
friction force at the contact line. Leh et al. [173] showed that stick and slip during
vertical deposition is due to the interplay between
YDF
and the surface tension at
the substrate-suspension-air contact line. They suggested that controlling particle
concentration, relative humidity and temperature are essential in reducing stick and
slip.
117
......
.....
. ................................
Fig. 5-1 shows the different surface tension forces during convective assembly.
The equation of motion of the contact line, L(t), for this set-up, is shown in eq. 5.1.
Figure 5-1: Plot of the surface tension forces during convective assembly. The suspension is withdrawn at a rate v.
P
d2 L
=
YDF -
YSCOS(9) +
&vz
-
pg.
(5.1)
Here, p is the density of the suspension, q is the viscosity of the suspension,
vz is the z-component of the velocity of the suspension, and g is the gravitational
acceleration. This is similar to the analysis presented by Won et al. [176].
Won et al. [176] recently showed that stick and slip can be avoided when colloidal
films are assembled through Langmuir-Blodgett (LB) technique at high humidity
and high concentration of particles. They found that the final particle density on
the template is significantly lower than the initial particle density at the air-water
118
interface. In their experiments, transfer efficiencies were 0.19±0.04* when a template
with holes arranged in (100) symmetry was used. They also showed that the transfer
efficiency decreases with an increase in the lifting speed of the substrate. In their
model, they assumed that at high humidity, water does not evaporate during selfassembly. With this assumption, their analysis showed that
#,
the particle area
fraction in the monolayer on a template, is given by eq. 5.2:
# = #0 +
Here,
D2
B9Y
-)
c -Cos (0) 09#
0
=0. (
6,qU
+ pg).
D6
(5.2)
#0 is the particle area fraction in the monolayer on the solvent (i.e.
far away
from the contact line), D is the particle diameter, c is an adjustable parameter, U
is the velocity at which the template is withdrawn during LB assembly, and 6 is the
wetting film thickness. In the sparse pattern, fig. 4-6,
0
# is 0.22.
The corresponding
, according to eq. 5.2, is 0.24 for particles with D = 250nm. This corresponds to
a concentration of 5 x 1012 particles/m 2 . For this calculation, it was assumed that
6 = D, U = 1mm/min, c -cosO = 15.15 x 10-15, and 87y/&q# = -3.2 x 10-4mN -m.
In comparison, if an isotropic distribution of particles is assumed during convective
assembly, the concentration at the air-solvent interface is 9.77 x 1010 particles/m2 t
-assuming
a volume concentration of 0.025-v/v%. This indicates that a lower
#o
may be required during LB assembly.
According to eq. 5.2, a lower
#o can
be used if the second term on right side of
eq. 5.2 is decreased. This indicates that during LB assembly of particles, it is ideal
to have transfer efficiency as close to 1.0 as possible. As shown by Won et al. this
is possible if the colloidal film is assembled at a lower U. At very low U, it may be
possible to ignore the entire second term on the right side in eq. 5.2 and obtain transfer
efficiency close to 1.0. Clearly, in this regime, the final arrangement of particles on the
template will also be influenced by the interaction between particles. Additionally, a
high humidity may be required to avoid stick and slip during deposition.
*Transfer efficiency is defined as the ratio of the density of particles assembled on a template to
the density of particles on the air-solvent interface.
tThis corresponds to a 40 = 0.0048
119
Besides LB method, spin coating [177] and hydrodynamic flow of particles [145]
can lead to domains without stick and slip. However, both these methods are kinetically driven, where the particles are forced to arrange in or between surface features
due to rapid solvent evaporation or flow. Additionally, a high concentration of particles is required. Therefore, these may not lead to the formation of the sparse pattern.
120
Chapter 6
Monte Carlo Simulations of Sparse
Ordering
A number of methods exist to predict the nucleation of stable colloidal phases [2,
100]. Researchers have often relied on free energy calculations to predict the most
stable colloidal structures. They have shown that when the potential in a colloidal
system is repulsive, packing arguments and entropy alone are sufficient to cause bulk
crystallization of stable phases [123].
Contrary to this argument, in chapter 4 it was shown that sparse structures do
not nucleate at high rnR, irrespective of the concentration of particles. To investigate
this further, detailed Monte Carlo simulations are discussed in this chapter. These
show that the final order in fig. 4-6 results from an interplay of the concentration
and electrostatic repulsion between particles.
In Monte Carlo methods, random system changes are rejected or accepted according to predefined rules. The scheme followed here is the Metropolis algorithm
[179]. In this scheme, a change is always accepted if it results in lower system energy.
However, it is only accepted with a Boltzmann probability, if it leads to an increase in
the total system energy. These rules satisfy the conditions of detailed balance, which
states that the number of transitions from state A to state B must equal the number
of transitions from state B to state A. More detailed information about Monte Carlo
schemes can be obtained elsewhere [180].
121
The internal energy in a colloidal system is obtained by a pairwise summation
of the interaction energy. In a canonical ensemble (NVT system), the movement of
a particle leads to a change in the internal energy AU. The acceptance rules for a
transition in such a system from Ai to Bi are:
acc(Ai -+ B) = 1
(6.1)
a cc(Aj --+ B ) = exp(- ETiAU').
(6.2)
AUS < 0
AUz > 0
In a grand canonical ensemble (pVT), in addition to the movement of particles,
the internal energy can change due to creation or destruction of a particle. As a
result, there are additional acceptance rules. These are:
For particle creation:
AUz - ptT < 0
AU, - pLT > 0
acc(Ai
(6.3)
acc(A --+ Bj) = 1
-*
E
B ) = exp(
giaU-
kBT
pT)
(6.4)
and for particle destruction:
AUi + pT < 0
AU + pT > 0
acc(Ai
-*
Bi) = 1
acc(Ai -- B ) = exp(-
EsgiU
kBT + puT
(6.5)
(6.6)
where p is the chemical potential.
6.1
Simulation Set-up
Simulations were conducted to verify the formation of a sparse pattern of polystyrene
(PS) particles, discussed in section 4.3. The templated assembly set-up described
122
in chapter 4 is best simulated by a grand canonical ensemble. Indeed, the template
represents a system where particles may enter or leave at will; this is dictated by
the chemical potential and the volume of the suspension. Thus, a grand canonical
ensemble was chosen for the Monte Carlo (MC) simulations. The simulation box is a
template with holes arranged in a square pattern, akin to fig. ??. For the current setup, the simulation template had 24 x 24 sites. All templates were tested with periodic
boundary conditions. Since A2 > 1, the final arrangement of colloidal particles is non
close packed, even when all the holes are occupied. Thus, vdW interactions can
be ignored. As a result, internal energy is given by a pairwise summation of the
electrostatic energy only. The picture that emerges is that of an Ising model type
system, with each site either with or without a particle.
MC simulations were carried out to obtain optimal arrangement of 140 nm, 250
nm and 500 nm sized PS particles. Corresponding pitches for the templates were 185
nm, 330 nm and 660 nm, respectively. A colloidal dispersion is characterized by K-1
in the solvent, the concentration of particles in the suspension and temperature, T.
Thus, for each particle type, MC runs were carried out when r-' = 30 nm, 100 nm
and 204 nm.
The phase boundary between sparsely ordered phase and the phase where all sites
on the template were occupied, was tracked by the change in a translational order
parameter, r. r [181, 182, 183], was computed over T - p phase space, at constant
K-1.
The translational order parameter, -r,is given by eq. 6.7 [183]:
= -1
SC
Ig(s) - 11ds,
(6.7)
sc JO
where g(s) is the pair distribution function, and s = rp1 / 3 , is the radial distance
scaled by the number density, and se is a numerical cutoff. In this work sc=6.0.
For each MC set-up, initial arrangement of particles was chosen by randomly
deciding if a site is occupied (that is, if it has a particle), or vacant. A thousand
MC steps were run before recording any data. Fluctuations in the system energy
were negligible after 1,000 steps. A further 2,000 steps were run to gather data after
123
initialization. During each of these steps, system energy and arrangement of the
particles were recorded.
6.2
Simulation Results
The energy of a configuration depends on the electrostatic interaction between particles and the chemical potential energy of the system. Electrostatic energy is calculated
as a pairwise summation of the Yukawa interaction between particles. On the other
hand, the chemical potential energy is proportional to the concentration of particles
and the temperature of the system. It is given as a product between the chemical potential for the system and the average number of particles on the template.
Mathematically, the system energy is written as:
Usystem
=
(6.8)
UYukawa + y x Nay9 ,
where
(6.9)
p= kB x T x lin(c).
Although
T
was tracked over I - T space, it is more instructive to look at changes
in r in the concentration-T landscape.
The system energy varied smoothly over
p - T and concentration-T phase spaces. As a result, nucleation of a new phase
was undetectable from energy plots. On the other hand,
T
showed discontinuous
variation over p - T. Since p is proportional to concentration, c, these discontinuities
were observed on the c - T landscape too. This indicates that there might be one or
more phase transitions in the system.
For all particle sizes, when ,-1 was 30 nm, electrostatic interaction between particles was weak. Thus, system energy was dominated by the chemical potential energy.
As a result, configurations where all sites on the template were filled, were stabilized
over all others. For 140 nm particles, this is seen in the contour plot of
T
(fig. 6-1).
Here, r = 1.1, when all sites on the template are occupied. This configuration is
labeled and is stable over most of the plot. When r-7 is 100 nm, the configuration
124
-
----------
. .....
. .......
......
when all sites on the template are occupied, is stable over a smaller region in the c - T
landscape (fig. 6-2). Finally, when K-' is 204 nm, the configuration when all sites on
the template are occupied, is stable over a very small region in the c - T landscape
(fig. 6-3). Similar plots are shown for 250 nm and 500 nm particles in fig. 6-4-fig.
6-6 and fig. 6-7-fig. 6-9 respectively.
When ,
1
is 204 nm, there are numerous features on the c - T landscape; many
phases may be stable. For a better understanding, a brief discussion for the arrangement of particles at different T, r-1=204 nm, and ln(c)=40.1 is presented.
1.15
40
Phase with all sites
on the template occupied
30
9%Ift
20
10
0
0
600
T/10 [K]
800
1000
0.45
Figure 6-1: Plot of r across In(c) - T landscape, for the arrangement of 140 nm
particles, when
6.3
-1=30 nm
Discussion
The variation in the arrangement of 140 nm, 250 nm and 500 nm particles at K-1
= 204 nm and ln(c) = 40.1 is presented in fig. 6-10 - 6-13, fig. 6-14 - 6-17 and fig.
6-18 - 6-21 respectively. In these figures, solid red circles represent an occupied site,
whereas an empty circle represents an empty site. A pair distribution function (PDF)
for each arrangement is plotted next to its respective figure.
125
....
..
...
.. ....
..
1.55
40
30
20
10
0
0.44
400
600
T/10 [K]
Figure 6-2: Plot of r across ln(c) - T landscape, for the arrangement of 140 nm
particles, when r-1=100 nm
1.50
40
30
20
10
0
0.34
400
600
T/I0 [K]
Figure 6-3: Plot of r across ln(c) - T landscape, for the arrangement of 140 nm
particles, when r-1=204 nm
126
....---------...........
.. ...
....
....
......
....
..............
................
....
....
............. .......
1.50
40
30
20
10
0
0.34
200
0
400
600
T/10 [K]
800
1000
Figure 6-4: Plot of r across ln(c) - T landscape, for the arrangement of 250 nm
particles, when n-1=30 nm
1.3
40
30
20
10
0.50
.
0U
0
200
400
600
800
1000
T/10 [K]
Figure 6-5: Plot of r across ln(c) - T landscape, for the arrangement of 250 nm
particles, when K-1=100 nm
127
. ..........
.........
......
....................
.........
.......
.............
...
......
1.67
40
30
20
0
0.47
200
0
400
600
T/I0 [K]
800
1000
Figure 6-6: Plot of r across ln(c) - T landscape, for the arrangement of 250 nm
particles, when
'-1=204nm
1.63
40
Phase with all sites
on the template occupied
30
% 20
10
1.5
I1.2
0.83
0
0
200
400
600
TI10 [K]
800
1000
Figure 6-7: Plot of r across ln(c) - T landscape, for the arrangement of 500 nm
particles, when n-1=30 nm
128
.................
.............................
.....................
................
...
....................................................................................................
........
...........................
1.7
40
30
20
10
0
0
200
400
600
g00
0.69
10
1000
T/I0 [K]
Figure 6-8: Plot of r across ln(c) - T landscape, for the arrangement of 500 nm
particles, when i,-1=100 nm
1.61
40
30
20
10
0
200
400
600
800
1000
0.68
T/10 [K]
Figure 6-9: Plot of r across ln(c) - T landscape, for the arrangement of 500 nm
particles, when n-1=204 nm
129
At T=1100K, nuclei of a sparser structure (similar to fig. 4-20) are visible in the
arrangement of 140 nm (fig. 6-10) and 250 nm (fig. 6-14) particles. In comparison,
500 nm particles arrange randomly. Their arrangement at T=1100 K is shown in
fig. 6-18. At T=3100K, nuclei of sparse structure are stabilized for all particle sizes.
Fig. 6-11, fig. 6-15 and fig. 6-19 show the arrangement of 140 nm, 250 nm and 500
nm particles at 3100 K, respectively. Sparse domains of 140 nm (fig. 6-12) and 250
nm (fig. 6-16) particles remain stable up till T=5100K; sparse domains of 500 nm
particles start to shrink at T=5100 K (fig. 6-20). Finally, when T=7100K, the sparse
structure disappears completely and is replaced by a structure in which all sites are
occupied. Fig. 6-13, fig. 6-17 and fig. 6-21 show the arrangement of 140 nm, 250 nm
and 500 nm particles at 7100 K, respectively.
For all particle sizes, the sparse structure is stable up to T ~3100K, when r-1=100
nm, and not stable at all when r--1=30 nm. These simulations show that decreasing
K-1 reduces the size of domains with sparse arrangement of particles. This agrees
with the experimental observations discussed in chapter 4. As a result, it can be
inferred that although entropy maximization may have a role to play in stabilizing
the sparse structure, the key role is played by the high Debye length in the system
and a low concentration of particles.
Fig. 6-10 and fig. 6-14 show that small domains with sparser structure can also
be nucleated if the concentration of particles is low. However, as seen in fig. 4-20,
stabilization of large domains with this structure, requires an even higher
130
-.
...................
- 11
.....
..
.... ..
..
oooo0o0o0oo0o0oo
0000000000000000
x- =204 nm
000000000 00000
00e0e0eo0eo000eo
g(r)
*OOOOOOOOOOOOOOOO
.o0oo0ooo0o0oooo
-
x- 2""
=100nm
r =30
= n
3
QQ*Q*Q*QQ*QQ*QQ.
2
oo0o0ooo0oo0oo0o
OOO O0OO OO OOOO
0I..........
0
2
4
rOO
6
a
10
Figure 6-10: (a)Arrangement of 140 nm particles at ,- 1 =204 nm, ln(c)=40.1 and
T=1100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
K-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF
plots show that unlike at ,-1=204 nm, at ,-1=30 nm, all sites on the template are
occupied.
OOOO OOOOO
OOOOOOOO
0ooo
@OO
OO
OO
oo
o
0
o
o
O
o0o0oo.O.oo0o0oO
.o0o0o0oo0o0o0o.
o0o0o0o..o0o0oo.
OOOOOOOOOO0
*oeoeeoeoeoeoeoe
OQOQOQOQ
O
**
-1204nm
i1
0-
O
=l100nm
,=aonm
g(r)
4
3
2
0
2
4
rIo
6
a
10
Figure 6-11: (a)Arrangement of 140 nm particles at ,-1=204 nm, ln(c)=40.1 and
T=3100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
K-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF
plots show that unlike at ,-1=204 nm, at ,-1=30 nm, all sites on the template are
occupied.
131
OO@OOO@OOOOO
=204nmn
t
@@O@OOOOOO
g(r)
.o0o0o0o0o0o0o0o
.. o0o0o0o0o0o0o.
.o0o0o0o0o0o0o..
m=30m
__"
3
1
@@OOOOOOO
.o0o0o0o0o0o0o..
o0o0o0o0o0o0o0o.
0
0OSO@O@OOOOOO
riO
2
8
6
Figure 6-12: (a)Arrangement of 140 nm particles at ,-1=204 nm, ln(c)=40.l and
T=5 lOOK. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
K-1.=100 nm and 30 nm are plotted in blue and green respectively. These PDF plots
show that at ,c 1 =30 nm all sites on the template are occupied; many domains where
all sites are occupied, are also stabilized for ,- 1 =204 nm.
al
ste
0-=24
reocupe,0reasostbiiedfo
0000000000000
m
K-
4
'= 204nr
and
of 140 nm (r)particles at s--1=204 nm, ln(c)=40.1
Figure 6-13: (a)Arrangement
-1 = 30 nm
g00000001
template,
the
on
particles
the
for
(PDF)
Function
(b)Pair Distribution
T=5100K.
3
.o0o0o0o0o***o**
00000O000
PDF for the arrangement of particles at
comparison,
For
red.
in
plotted
(a), is
in
.o..o0o0o.0.o0o.
000O00O0O000O0O000
n-1100nm and 30 nm are plotted in blue and green respectively. These PDF plots
9000000000009
-, 0OOOO
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.
6
8
hr 1
9(rtemplate are occupied.aydman
OOOO0
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all sites on the
that at a-l=3 nmales
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00000000000O0000
00O
0000O000O0
O1112
4
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4 2-3mprice tn124nl~)4.
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132
1
6O
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Dpos
.................
.....
O000000000000000
OOOOOOOOOOOOOOO
0000000000000000
0O0OOO0OO0O0O0O0
000000o
0 *
-1204
g5)__
=
nm
3100 nm
___
4 9(r)
1=30nm
1=
0000000000000000
0000000000000000
o000000000000000
0000000000000000
0000000oo000000
00000000000000001
0o000000000000000
0000000000000000
0000000000000000
0**,
.
0
0000000000000000
2
4 riO
8
.
10
Figure 6-14: (a)Arrangement of 250 nm particles at ,-'=204 nm, ln(c)=40.l and
T=1100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
These PDF
K-1=100 nm and 30 nm are plotted in blue and green respectively.
1
are
template
the
on
sites
all
nm,
,-1=30
at
nm,
plots show that unlike at ,-~ =204
occupied.
0000000000000000
0000000000000000
0000000000000000
*000000000000
5
gKr)-
000
0000000000000000
0000000000000000
0000000000000000
.000000000000000
0000000000000000
0000000000000000
0000000000000000
00000000000000001
0000000000000000
-
c-= 204 nm
=i00nm
4
3
2
.0000000000000000
Figure 6-15: (a)Arrangement of 250 nm particles at ,-'=204 nm, lm(c)=40.1 and
T=3100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
100 nm and 30 nm are plotted in blue and green respectively. These PDF
K~plots show that unlike at ir-=204 nm, at ,-1=30 nm, all sites on the template are
occupied.
133
...........................
....
...........
.....
.....
..........
...
......
eeeeeeeeeeeeeo
O
O
O0O0-
4K-1=204nm
00000
0000
0000
x-I=
g(r)
0Q0Q0Q0Q0Q0Q0Q00
100 nm
=30n
___
3
0000000000000000
.o.o.o..o..o..o..
.. o.o.o..o..o.o.
0000000000000000
000000000000
eoeoo o@oo0
00o000o000o0o0o0
1
0O0O0O0O0O0O0000
*
000000000000000O
da
4
2
8
6
10
Figure 6-16: (a)Arrangement of 250 nm particles at r-1=204 nm, ln(c)=40.1 and
T=5100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
n-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF plots
show that at n-1=30 nm all sites on the template are occupied; many domains where
all sites are occupied, are also stabilized for - 1=204 nm.
09 9
9
00
0
9
6
000
0
04
0
__
0
--
000000 000000
00
*e@eee@eo
0000000
00O
nm
rl =100 nm
-- (r)
000O
K- = 20
"-=3
000000000000
00O0000O0O000000
0000O00000000000
0eeeeeeeeeeee
.......
2
-
0....0
Figre6-7:(aAraeenteo 25 nmprtce ati
1
4
m, lnc=4 an1d
T=7100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
,-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF plots
show that at all n- values, all sites on the template are occupied.
134
00000000000000
0000000000000000
5= 204 nm
O000000000000000
000000000000000
oe0ooooo0eoeooe
0000000000000000
0000000000000000
000000000000000
....
..
........
- - -
.
'0
. '_
I------ - -----"I'll,",
1=100 nm
-
g(r)
4
K-I=30""
3
0000.000000000
oeoooooooo~ooooo*
000000000000000
OO@OOOOOOOOOOO@
1A
000000000000000
00000000000000000
00000000* 0000000
0
4
2
8
,, 6
10
Figure 6-18: (a)Arrangement of 500 nm particles at ,- 1=204 nm, ln(c)=40.1 and
T=1100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF
plots show that unlike at -1=204 nm, at r- 1 =30 nm, all sites on the template are
occupied.
00000000000000
5
0000000000000000
o0o0o0o0o0o0o0o*
00000000000000
000000000.000000
=204n
-
000000000000000
4
-
g(r)
--
10nm
x13n
3
00000000000000002
00000000000000
000000000000000
00000000000000
1
000000000000000
0000000000000000
0000000000000000
0
*
2.
L
4
Figure 6-19: (a)Arrangement of 500 nm particles at r,-1=204 nm, in(c)=40.1 and
T=3100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
These PDF
K-1 =100 nm and 30 nmn are plotted in blue and green respectively.
plots show that unlike at r,-1=204 nm, at r,-1=30 nm, all sites on the template are
occupied.
135
I
-- ------------------
@@O
@O OO
00O
00O
O
0O
@OO0O
00O
-
-
=2nm
00O
00
0
00O0000
0O
-1= 100um
-1= 30 nm
g(r)
0
00000000~
00O00O0O0O000O00
2
0o0o000000000000
*oeoee
O
0
e
0
0
0
0
0
0
eeee
0
0
0
1OO
0
0
0
0
2
0
0
4
10
8
r
Figure 6-20: (a)Arrangement of 500 nm particles at r- 1=204 nm, ln(c)=40.1 and
T=5100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
K-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF plots
show that at r,-1=30 nm all sites on the template are occupied; many domains where
all sites are occupied, are also stabilized for K-1=204 nm.
0000000000000000
000*000
00000
00
0000
00
204 nm
4K-1=
(r)
00
000 000 000
000
-nm
-
30 n
*eeeeeoeeeoeeee
0000000000000000
2
0000000000000000
000000O000000000
00000000000000000
0
t
show00
aes,
0
0
0
t
on t
2
4
2
4
r/o
6
8
10
1
Figure 6-21: (a)Arrangement of 500 nm particles at rn-1=204 nm, ln(c)=40.1 and
T=7100K. (b)Pair Distribution Function (PDF) for the particles on the template,
in (a), is plotted in red. For comparison, PDF for the arrangement of particles at
K-1=100 nm and 30 nm are plotted in blue and green respectively. These PDF plots
show that at all r.-1 values, all sites on the template are occupied.
136
6.4
Conclusion
In summary, it was correlated with simulation that nucleation of stable sparse structures, akin to fig. 4-6 and fig. 4-20, takes place at high r
and low concentration
of particles. It was shown that electrostatic repulsion is the key to obtaining large
domains with sparse order. Moreover, sparser domains can be nucleated and stabilized over large distances if i-- is higher, and concentration of particles in the system,
lower. Although higher r,-- may not be achievable in aqueous suspensions, it can be
obtained in mildly polar solvents, like isopropanol or ethyl alcohol. Thus, in these
solvents it may be possible to nucleate and stabilize other sparser structures over
larger distances.
137
138
Chapter 7
Conclusions and Outlook
Among the many approaches to create non-close-packed structures, self-assembly is
appealing because it can create a colloidal crystal quickly and over a desired length
scale. In this thesis, lower symmetry structures were created by exploiting interparticle interactions between strongly charged particles.
It was shown that oppositely charged hydrophobic particles can be rapidly arranged into ordered 2D architectures through spin-coating. Calculations showed that
non-ionic amphiphilic surfactants create a steric barrier, that prevents these particles
from coagulating during self-assembly. Previously, only oppositely charged particles
with charge densities two orders of magnitude lower had been ordered. It was shown
that, at high Debye length and low particle concentration, a layer-by-layer method
can be used to create a non-close-packed arrangement of like-charged particles, on a
substrate of close-packed and oppositely charged particles.
Electrostatic repulsion between similarly charged colloidal particles was exploited
to nucleate and stabilize non-close-packed structures with sparse ordering on lithographically fabricated templates. It was shown that a 2D heterostructure can be
created by filling the remaining holes on the template with another particle type.
Two layers of a 2D heterostructure were created through layer-by-layer assembly.
In the end, one kind of particle was removed to create a two-layer non-close-packed
structure of silica particles. Stick and slip of the meniscus limited the overlap between
bands of particles during each deposition step. As a result, non--close-packed domains
139
were only a few micrometers large. Monte Carlo simulations confirmed that sparse
structures are nucleated only at high Debye lengths and low particle concentrations.
In addition, it was found that sparser domains can be nucleated at an even higher
Debye length and lower concentration of particles.
Implications from the above studies are many. Newer structures, which are more
robust compared to their like-charged counterparts, can now be fabricated from oppositely charged particles. These include binary structures or non-close-packed structures, like zinc blende. On the other hand, templates with different geometries may
be used to create multiple sparse structures.
The biggest challenge lies in arresting the effect of stick and slip. It was shown
that bands with sparse order were around 15 pm wide, although these were hundreds
of micrometers long perpendicular to the direction of meniscus slip. If stick and slip
can be arrested, it may lead to very wide bands. This may encourage the discovery
of newer self-assembly processes. Already, horizontal assembly reduces stick and slip,
but it provides no control over the thickness of colloidal crystals that are fabricated.
It may be that a combination of vertical and horizontal deposition is required to
overcome stick and slip.
Interest in the fabrication of crystals of colloidal particles with controlled packing,
symmetry, periodicity, crystal orientation and packing quality, is fueled by the need
for colloidal crystals exhibiting tailored structures in many applications. Methods
and results described herein constitute a step in this direction, allowing for the use
of self-assembly to fabricate novel non-close-packed structures.
140
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